
o °* 



'< -e 



** 







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* „ . 



THE PRACTICAL 



COTTON SPINNER, 



AND 



MANUFACTURER 



/37 6^9 

THE PRACTICAL 

COTTON SPINNER, 

AND 

MANUFACTURER: 



MANAGERS', OVERLOOKERS', AND MECHANICS' 
COMPANION. 

A COMPREHENSIVE SYSTEM OF 

CALCULATIONS OF MILL GEARING AND MACHINERY, 

FROM THE PRIMARY MOVING POWER, THROUGH THE DIFFERENT PROCESSES OF ' 

CARDING, DRAWING, SLUBBING, ROVING, SPINNING, AND WEAVING, 
With the recent improvements in Machinery. 

TO WHICH ARE ADDED, 

Compendious Tables of Yarns and Reeds for Silk, Linen, Worsted, and Wool, 
BY R\ SCOTT. 



(Etorotefc aafr jEnlaropfr, to tit plates of gCnuricarc JHacIjtru*, 
BY OLIVER BYRNE, 

CIVIL, MILITARY, AND MECHANICAL ENGINEER ; 

COMPILER AND EDITOR OF THE " DICTIONARY OF MACHINES, MECHANICS, ENGINE-WORK, AND 

ENGINEERING-;" AUTHOR OF " THE PRACTICAL MODEL CALCULATOR,'' AUTHOR OF " THE 

COMPANION FOR MACHINISTS, MECHANICS, AND ENGINEERS ;" AUTHOR AND INVENTOR 

OF A NEW SCIENCE, TERMED " THE CALCULUS OF FORM," A SUBSTITUTE FOR 

THE DIFFERENTIAL AND INTEGRAL CALCULUS ; AND NUMEROUS OTHER 

MATHEMATICAL AND MECHANICAL WORKS, ETC. ETC. ETC. 



PHILADELPHIA: 
HENRY CAREY BAIRD 

SUCCESSOR TO E. L. CAREY. 

1851. 




Entered according to the Act of Congress, in the year 1851, by 

HENRY CAREY BAIRD, 

in the Office of the Clerk of the District Court in and for the Eastern District of 
Pennsylvania. 



PHILADELPHIA *. 
T. K. AND P. G. COLLINS, PRINTERS. 



PREFACE 



Several publications on Cotton Spinning have appeared, the 
merits of which it is not my intention to discuss. As a practical 
working man, I may however observe, that those which have 
come under my notice are, to a considerable extent, destitute of 
much practical utility. The systems they contain of making the 
calculations, are not sufficiently explicit, and hence can never 
achieve the great and important object of combining practice 
with theory, which is so essential, particularly to managers and 
overlookers. 

The present work contains every necessary calculation con- 
nected with the most recent improvements in the machinery em- 
ployed in the spinning and manufacturing business. The rules, 
examples, and illustrations are simple and easily understood ; 
so much so that any person having a knowledge of the element- 
ary rules of arithmetic may, without difficulty, by a little atten- 
tion to the rules and examples, prepare himself to fill the impor- 
tant situation of overlooker or manager in any department of 
the spinning and manufacturing business. The rules and exam- 
ples are all original, and have been reduced to practice with 
great care. 

Calculations relative to the machinery used in the spinning and 
manufacturing of all fibrous substances, are attainable by the 
rules established in this work, so that it will be found equally 
beneficial to those engaged in the spinning and manufacturing of 
silk, flax, worsted, and wool. Compendious tables are arranged, 
accompanied with rules, examples, and illustrations, to show the 
size, girt, hank, or proportion of hank, in every operation. The 



VI PREFACE. 

fineness of yarns according to the different lengths, constituting 
the lea, cut, or hank, with the different systems of counting 
worsted reeds, are added. 

During my engagements for many years in the different de- 
partments of the cotton business, I found a great deficiency of 
theoretical knowledge among practical persons filling important 
situations in cotton and other factories. This led to the deter- 
mination, at the request and by the encouragement of several 
friends, to prepare a complete system of calculations ; and I have 
no hesitation in saying, that such a system will be found in the 
present work. And while it answers as a book of reference to 
the master, and an assistant to the manager, overlooker, and 
mechanic, it will convey instructions to the aspiring operative, 
and may be found a useful auxiliary in the tuition of young per- 
sons intended for the spinning, manufacturing, or machine busi- 
ness. This work will not only be found to convey a correct 
knowledge of its appropriate calculations, but, in following out 
the rules here laid down, a considerable degree of pleasure must 
be experienced when it is found that theory and practice are so 
beautifully combined, and that it will enable persons to give 
general satisfaction in the management of their respective de- 
partments of this peculiarly important business. 

It has been remarked, that u the country which parts with the 
raw materials of labor, is afterwards bereft of the sustenance of 
man — food goes away to visit industry, and hunger remains to 
dwell with idleness, and famine descends, with all its terrors, to 
castigate the folly which blindly relinquishes the material of 
manufactures." 

Foreign manufactures are the destruction of any country ; 
and we believe, the people may stop or retard that destruction 
by superseding such manufactures, by producing articles equally 
good and cheap. A divided people, it is manifest, cannot pur- 
chase victory in war ; the industrial prosperity of peace is equally 
impossible to a people who are at war with each other. Besides — 
let us not blink the truth — the nations that have distinguished 
themselves in industry and commerce, had always first distin- 



PREFACE. Vll 

guislied themselves in arms for freedom. When the Persian 
was chased from the shores of Greece like a wolf, the republican 
Greek became a great trader. 

The Saracens' conquests gave place to their commerce ; after 
the scimitar came the shuttle. The Dutch laid down the arque- 
buse to assume the tiller. The Italians of their republican ages 
relieved guard alternately at the rich loom and the Goth-defying 
bastion. 

However, it requires not a prophet's inspiration to foretell that 
the day is fast approaching when none but the superabundant raw 
material will be shipped from this country. The South and West 
have made more than a beginning in manufacturing their own 
cotton, iron, hemp, flax, &c, and the North and East can more 
than vie with Europe in wonder-working machinery. I have 
held these opinions for some time, and am much strengthened in 
them, on reviewing the vast improvements introduced into the 
cotton manufacturing business by American machinists and engi- 
neers. I may particularize the Niagara Throstle, or McCulley's 
patented improved Spinning Frame ; Mason's Self-acting Mule ; 
Judkin's Heddle Machine. Respecting these machines we have 
entered into particulars, and have given large working drawings 
of them. 

I should have mentioned the Cop-spinner of Dodge and Sons, 
of Dodgeville, Attleborough, Massachusetts. This first class 
machine will wind the yarn as fast as twisted, or when properly 
twisted, upon each of the spindles in a regular or proper shaped 
cop, which shall have a binding thread between each two adja- 
cent layers of yarn, which prevents the cop from falling apart 
while being removed from the spindle. 



CONTENTS 



MILL GEARING, &o. 

Revolutions of Shaft a minute 
Revolutions of Beater at Blowing Machine a minute 
Revolutions of main Cylinder of Carding Engine 
Revolutions of Counter Shaft a minute 



Page 

9 

22 

23 

24 



ON MIXING COTTON. 



Observations on 



25 



ON MACHINERY. 

Observations and Rules for working Speeds, &e . . 26 

Willow, Particulars of . . . . .26 

Blowing Machine . . . . . .27 

Dimensions of a double Blowing Machine, including speeds, tra- 
versing of Rollers, &c. . . . .35 

Lap Machine ... . . . .35 

Particulars of Lap Machine, including speeds, intermediate 

draughts, total draughts, &c. . . . ,48 

Carding Engine, Observations on . . .48 

Speeds, intermediate draughts, total draught, consumption, pro- 
duction, &c. ...... 49 

Particulars of a Carding Engine . . . ' 70 

Drawing Frame, speeds, intermediate draughts, total draughts, 
consumption and production at each head, weight of Cotton, 
and length of Carding required to supply the first head of 
drawing, &c. ...... 71 



CONTENTS. 



Particulars of Drawing Frame .... 91 

Tube Frame, Observations on .... 92 

Speeds, intermediate draughts, total draught, consumption, pro- 
duction, &c. . . . . . .92 

Particulars of a Tube Frame ..... 110 

Slubbing Frame, speeds, intermediate draughts, total draught, 
consumption and production, turns per inch, size, girt, or 
hank of slubbing, &c. . . . . .111 

Roving Frame, speeds, intermediate draughts, total draught, 
consumption of slubbing, production of roving, size, girt, or 
hank roving, loss sustained in working, turns per inch, &o. . 123 
Throstles, Observations on . . . .132 

Speeds, intermediate draughts, total draught, production, &e. . 133 
Particulars of Throstle . . . . .143 

Mules, speeds, intermediate draughts, total draught, gain at 
carriage, consumption of Roving, production of Yarn, turns 
per inch, &c. ..... 144 

Tables, showing the Weight of Carding and Drawing, according 
to the length, weight, and size or girt in each operation, with 
rules and examples . . . . .164 

Table, showing the dividend for any number of inches from 1 to 
36, whereby the Weight of Cotton required to be fed on the 
Feed Cloth at the Lap Machine may be ascertained for any 
numbers of Yarn, according to the proportion of the hank at 
the Lap Machine, with rules and examples . . .177 

Tables of Carding, Drawing, Slubbing and Roving, with rules 

and examples; Change Wheels, &c. . . .178 

Self-acting Mule, revolutions of all the different movements per 
minute, intermediate draughts, total draught, traverses, pro- 
duction, turns per inch, &c. &c. . . . . 192 

Particulars of the Self-acting Mule, with observations, &c. . 228 

Hank or proportion of Hank in each and every operation from 

the Spinning to the Lap Machine .... 230 

Loss in working Cotton ..... 235 

Table of multipliers for ascertaining the loss sustained in work- 
ing any given length, or weight of Cotton, &c. . . 244 



CONTENTS. 



XI 



Loss in working any given length, or weight 

Average Cop and weight of Sets 

Spinner's Book, &c. . 

Dressing Machine, speed, &c. 

Particulars of Dressing Frame 

Power Loom, speeds, weight of Yarn required for a piece of 
Cloth, &c. . 

Wheels required to produce any given draught, &c. 

Wheels required to produce any given draught, &c, by cancel- 
ling ....... 

Reed Tables, explanation . 

Reed Tables, different systems of counting Reeds brought into 
conjunction with each other, with rules and examples 

Manufacturing of Cotton, Silk, &c, weight of Warps and Weft 
required for any fabric of Cloth .... 

Linen Yarn Tables, different Reels .... 

Linen Yarn Tables, showing the weight according to the num- 
bers or fineness of Yarns, and the different lengths weighed, 
with rules and examples ..... 

Linen manufacture, Yarns required to produce any fabric of 
Cloth . . . . 

Worsted and Woollen Yarns, Observations on, with explanation 
to the Yarn Table ...... 

Tables of Worsted and Woollen Yarns, showing the weight of 
one hank, dozen, and gross, according to the fineness, with 
rules and examples for ascertaining the length and weight 
of Yarns for any fabric of Cloth, &c. 

Worsted Count of Reeds, Observations on, and explanation of 
Reed Tables 

Worsted Reed Table, with rules, examples, &c. 

Miscellaneous Questions and Examples 

Rule and Examples for changing light Gearing to heavy, or 
heavy Gearing to light 

C. J. Judkins' American Healds, or Heddles . 

Mason's Self-acting Mule 

Niagara Throstle or McCulley's Spinning Frame 

Plates I. II. III. IV. V. VI. VII. VIII. 



Page 
246 

247 
255 

257 
262 

263 
271 

282 
293 

295 

306 
336 



337 
364 
367 

368 

380 

381 
386 

396 
398 
399 
416 
416 



THE 

PRACTICAL COTTON SPINNER 



AND 



MANUFACTURER 



MILL GEERING. 



Opinions relative to the best speeds for machinery may differ ; 
however, the following speeds are such as are generally adapted 
to machines spinning medium numbers ; but all machinery must 
be speeded according to the quantity required. 

RULES FOR WORKING SPEEDS OF SHAFTS. 

Multiply the strokes of the steam engine, or revolutions of the 
waterwheel, by the number of teeth in the wheel fixed on the 
first moving power, or given shaft, for a dividend, and divide by 
the number of teeth in the wheel fixed on the intended driven 
shaft, and the quotient will be the speed or revolutions of shaft 
required. 

To find the speed of any given shaft, ivhen the speeds of the 
intermediate shafts are not required. 

Multiply all the driving wheels together respectively, so far as 
the shaft you want the speed of, and that product by the strokes 
of the engine, the revolutions of the waterwheel, or any shaft: 
the speed being known for a dividend, then multiply all the 
driven wheels together accordingly, for a divisor, and the quo- 
tient will be the speed, or revolutions of the shaft required. 

If a steam-engine makes 22 double strokes a minute (that is 
the same as to make the crank revolve 22 times a minute) with 
a wheel fixed on the crank, or fly-shaft, containing 106 teeth ; 
what revolutions will the first or main line of shafts make, if the 
wheel with 106 teeth works into a wheel on the first or main line 
of shafts with 47 teeth ? 
2 



10 SPEED OF SHAFTS, 



22 strokes or revolutions each minute. 
106 teeth in wheel of crank or fly-shaft. 



132 

220 



Teeth of wheel on > 4T)2 332(49.617 revolutions a minute of first 
mam line of snait S -too • v c i» jv 

} 188 or main line of shafts. 



452 
423 



290 

282 



80 
47 



330 
329 



1 

If a wheel with 61 teeth be fixed on the first or main line of 
shafts, which makes 49.617 revolutions a minute ; what revolu- 
tions a minute will a cross-shaft make with a wheel 57 teeth 
fixed on it, worked by the wheel with 61 teeth? 

49.617 revolutions of shaft a minute. 
61 teeth in wheel or shaft. 



49617 

297702 



Teethof wheel on ) 57)3026.637(53.098894 revolutions of cross- 
cross-snatt 2g5 ghaft ft minute? or 

510 53.1— nearly. 



176 456 

171 

— — 540 

563 513 



513 

50 
456 



: 270 

507 228 



42 



SPEED OF SHAFTS. 11 

If a wheel with 75 teeth be fixed on a shaft revolving 49.617 
times a minute, works into a wheel with 41 teeth, fixed on a 
shaft for driving looms ; what number of revolutions will it make 
a minute ? 

49.617 revolutions of shaft a min. 
75 



248085 
347319 



IVf^ViZ^ 1 \ 41)3721.275(90.7628 revolutions a min- 
for driving looms J ^ ^ ute of shaft driving 



looms. 



312 

287 



257 
246 



115 

82 



330 
328 



If a wheel with 52 teeth be fixed on a shaft making 90.7626 
revolutions a minute, works into a wheel with 41 teeth, on the 
foot of an upright-shaft for driving mules; what revolutions a 
minute will the upright-shaft make ? 

90.7628 revolutions of shaft a minute. 
52 teeth of wheel on shaft. 



1815256 
4538140 

47196656 



12 SPEED OF SHAFTS. 

Teeth of wheel on^ 

foot of upright- V 41)47196656(115.1138 revolutions a minute 

shaft, J 41 of upright-shaft, driv- 

ing mules. 

61 
41 



209 

205 



46 
41 



56 
41 



155 
123 



326 

328— nearly. 

If a drum, 20 inches diameter, be fixed on an upright-shaft, 
for driving mules, which makes 115.1138 revolutions a minute; 
what revolutions will the upright-shaft in wheelhouse for driving 
rim or fly-shaft make, if a pulley, 12 inches in diameter, be fixed 
on a shaft, and worked by a strap from the drum 20 inches di- 
ameter ? 

115.1138 revolutions a minute, upright- shaft. 
Th^d'm^l ^ inches diameter of drum on shaft. 

uVS-sL™ ^2)2302.2760 

in wheelhouse, J i 9 i. 8 563 revolutions of upright-shaft ^ a 

minute in wheelhouse, for driv- 
ing rim-shaft. 

If a wheel with 61 teeth be fixed on the first or main line of 
shafts, making 49.617 revolutions a minute ; what number of 
revolutions will an upright-shaft make, with a wheel 57 teeth 
fixed on it, worked by the wheel of 61 teeth? 



SPEED OE SHAFTS. 13 

Teeth in wheel on ^ 4 „ 6n L min> of main . shaft 

mam-shalt working I ~.. 

into wheel on foot of j * * 

upright-shaft, J 49617 

297702 
Teeth of wheel on foot 1 5 —— 53<098894 revolSj min _ 
of upright-shaft, / ^ g5 ute of upright- 

shafts. 

176 
171 



563 
513 

507 
456 



510 

456 



540 
513 



270 

228 



42 

If a wheel with 70 teeth be fixed on the top of an upright- 
shaft making 53.098894 revolutions a minute, and works into a 
wheel with 39 teeth on a lying- shaft; what revolutions will the 
lying-shaft make a minute? 

53.098894 revols. of upright-shaft a minute. 
70 teeth in wheel on upright-shaft 

3716.922580 



14 



SPEED OF SHAFTS. 



Teeth of 
wheel on ly- 
ing-shaft, 



39)3716.922580(95.3057 revolutions of lying- 
351 shaft the minute. 



206 
195 



119 
117 



222 
195 



275 
273 

2 



If a drum 30 inches diameter be fixed on a shaft making 
95.3057 revolutions a minute; what number of revolutions a 
minute will a shaft make with a drum fixed on it 18 inches dia- 
meter, worked by a strap from the drum 30 inches diameter? 
95.3057 revolutions of shaft a minute. 
30 inches diam. of drum. 



Inches diam. 
of drum. 



| 18)285.91710(158.8428 revolutions of shaft a 
* 18 minute. 



105 

90 

159 
144 

151 
144 



77 
72 

51 

36 



150 
144 

6 



SPEED OF SHAFTS. 15 

If a drum 45J inches diameter be fixed on a shaft making 
95.30558 revolutions a minute; what number of revolutions a 
minute will a shaft make with a pulley fixed on it 13f inches 
diameter, and driven by a strap from the drum 45J inches dia- 
meter ? 

95.30558 revolutions of shaft. 
45.5 diameter of drum. 



47652790 
47652790 

38122232 



of^ufleT* I 13 -'< r 5)4336.403890(315.3748 revols. of counter- 
P J? J 4125 shafts a minute, 

■ driving blowing 

2114 and lap machines* 

1375 



7390 

6875 

5153 
4125 

10288 
9625 

6639 
5500 

11390 
11000 

390 

If a drum 36 inches diameter be fixed on a shaft making 
315.3748 revolutions a minute ; what number of revolutions will 
the beaters of a blowing machine make, if a pulley 6 inches 
diameter be fixed on the end of the beaters, and driven by a 
strap from the drum 36 inches diameter? 



16 SPEED OE SHAFTS. 



315.3748 revolutions of counter-shaft a minute, 
36 inches diameter of drum on shaft. 



18922488 
9461244 



Diam. of pul-*) ■ ■ ■ ■ - — 
ley on beat- V 113534928 

ers, 6 inches, J 

1892.2488 revolutions of beaters a minute. 

If a wheel with 62 teeth be fixed on a shaft making 53.098894 
revolutions a minute ; what number of revolutions will a shaft 
make with a wheel 46 teeth fixed on it, and driven by the wheel 
with 62 teeth? 

53.098894 revolutions of given shaft a minute. 
62 teeth in wheel on given shaft. 



106197788 
318593364 
Teeth of 



wheel on I 46)3292.131428(71.568074 revolutions of shaft 
shaft, J 322 minute. 



72 
46 



261 
230 



313 

276 



371 

368 



342 

322 



208 

184 



24 

If a wheel with 63 teeth be fixed on a shaft making 71.568074 
revolutions a minute; what number of revolutions will a shaft 



SPEED OF SHAFTS. 17 

make with a wheel of 45 teeth fixed on it, and driven by the 
wheel of 63 teeth? 

71.568074 revolutions of shaft a min. 
63 teeth in wheel. 



214704222 
429408444 



Teeth of wheel on ) 45) 45 08.788662(100.1953 revolutions of shft. 
snatt ' > 45 a minute driving 



looms. 



087 
45 



428 
405 

238 

225 



136 
135 



If a wheel with 49 teeth be fixed on a shaft making 100.1953 
revolutions per minute, drives a wheel of 38 teeth, fixed on foot 
of upright-shaft ; what revolutions will the upright-shaft make a 
minute ? 

100.1953 revol. of given shaft a minute. 
Teeth of wheel on shaft 49 



9017577 
4007812 

Teeth of wheel on } 

foot of upright- V 38)4909.5697(129.2 revolutions of upright- 
shaft, ) 38 shaft a minute — Spin- 

ning-room. 

110 
76 



349 76 

342 78— nearly. 



18 SPEED OF SHAFTS. 

If a drum 21 inches diameter be fixed on an upright-shaft, 
for driving upright-shaft in wheelhouse, making 129.2 revolutions 
a minute ; what number of revolutions a minute will the upright- 
shaft in wheelhouse make, with a pulley 14 inches diameter fixed 
on it? 

129.2 revol. a min. of upright-shaft. 
21 inches diameter of drum on it. 



1292 
2584 



Inches diam. of pulley, 14)2713.2(193.8 revolutions of upright- 

14 shaft in wheelhouse a 

minute, working rim or 



131 fly-shafts. 

126 



53 

42 

112 
112 



If a wheel with 60 teeth, fixed on a shaft, makes 53.098894 
revolutions a minute; what number of revolutions per minute 
will an upright-shaft make, with a wheel of 44 teeth fixed on its 
foot, and driven by the wheel of 60 teeth? 

53.098894 revolutions a minute. 
60 teeth wheel. 

Teeth of wheel on } 

foot of upright- V 44)3185.933640(72.40758 revol. of upright- 
shaft, ) 308 shaft a min., for 



105 
88 

256 

179 220 

176 

364 

333 352 

308 

. 12 



Dressing-room. 



SPEED OF SHAFTS. 19 



Or thus, dividing by 4 and 11 for 44. 
4<j 3185.93364 

11 ] 79648341 



72.40758—12 



If an upright-shaft makes 72.40758 revolutions a minute, with 
a wheel of 75 teeth fixed on top, working into a wheel of 41 teeth, 
fixed on a lying-shaft; what revolutions a minute will the lying- 
shaft make ? 

72.40758 revols. of upright-shaft a min. 
75 teeth of wheel. 



36203790 
50685306 



M^haft 11661011 I 41 )54.3056850(132.4529 revolutions a min. of 
^ £"" 41 shaft driving Dress- 



133 
123 



ing-frame. 



100 

82 



185 
164 



216 

205 



118 

82 



365 

369 — nearly. 

The speed of any shaft may be obtained, without ascertaining the 
speeds of the intermediate shafts, by the following 

RULE. 
Multiply the number of double strokes of the steam-engine, or 
the number of revolutions of any given shaft per minute by the 



20 



SPEED OF SHAFTS. 



number of teeth in the driving-wheels respectively, or, if drums 
or pulleys, by the inches in the diameters respectively, or in the 
place they occur, for a dividend, and all the driven-wheels, drums, 
or pulleys, in the same manner, for a divisor, and the quotient 
will be the speed of the shaft required. 

If a steam-engine be making 22 double strokes or revolutions 
a minute, with the following driving and driven-wheels, drums, 
and pulleys ; what number of revolutions a minute will the shaft 
make which is intended to drive a blowing machine or scutcher ? 



DRIVING. 

Revolutions a minute, crank 
or fly-shaft 22. 

Wheel on crank or fly-shaft 
106 teeth. 

Wheel on first lying-shaft, driv- 
ing upright-shaft 61 teeth. 

Wheel on top of upright-shaft 
TO teeth. 

Diameter of drum on shaft 45 J 



inches. 



DRIVEN. 

Wheel on first lying-shaft 47 

teeth. 
Wheel top of upright-shaft 57 

teeth. 
Wheel on next lying-shaft, 39 

teeth. 
Diameter of pulley on shaft for 

driving blowing machine 13| 

inches. 



22 revolutions a minute crank or fly-shaft. 
106 teeth in wheel on crank-shaft. 



2332 



2332 

13992 



61 teeth in wheel on first lying-shaft, driving 

upright-shaft. 



142252 

70 teeth in wheel on top of upright-shaft. 



9957640 



45.5 or 45 J inches diameter of drum on shaft. 



49788200 
49788200 
39830560 



453072620.0 dividend. 



SPEED OF SHAFTS. 



21 



47 teeth in wheel on first line of shafts. 
57 teeth in "wheel on foot of upright-shaft. 



329 
235 

2679 



39 teeth in wheel on second lying-shaft. 



24111 

8037 



104481 
13.75 or 13f inches diameter of pulley on shaft 

for driving blowing machines. 

522405 
731367 
313443 
104481 



1436613.75 divisor. 



1436613.75)453072620.0(315.375388 revolutions a minute, shaft 



430984125 

220884950 
143661375 

772235750 
718306875 

539288750 
430984125 

1083046250 
1005629625 

774166250 

718306875 



558593750 
430984125 

1276096250 



driving blowing machine. 



1276096250 
1149291000 

1268052500 
1149291000 

118761500 



22 SPEED OF SHAFTS. 

iV. B.—The small difference arising in the above system of work- 
ing r , is on account of working all the different speeds of shafts 
separately. (See former Examples.) 

If a drum 45J- inches diameter be fixed on a shaft making 
315.375388 revolutions a minute ; what number of revolutions 
will the beater of a blowing machine make, with a pulley fixed 
on the beater end, 10 inches diameter, and driven by a strap 
from the drum 45| inches diameter? 

315.375388 revolutions of shaft a minute. 
45.5 or 45J inches diam. of drum. 



1576876940 
1576876940 
1261501552 

Inches diam.") 

of pulley on V 10)14349.5801540 

beater end, J 

1434.9580154 revolutions of beater a min. 

If a shaft makes 84 revolutions a minute, with a wheel of 60 
teeth fixed on it, working into a wheel on a cross or upright-shaft, 
with 52 teeth ; what number of revolutions will the cross or up- 
right-shaft make? 

84 revolutions of shaft a minute. 
60 teeth in wheel on shaft. 



Teeth of wheel on cross 1 52)50 40(96.923 revols. of cross or up- 
or upright-shaft, / > 46g ^ ri ght-shaft a minute 



360 
312 

480 
468 

120 
104 

160 
156 



SPEED OP SHAFTS. 23 

If a cross or upright-shaft be making 96.923 revolutions a 
minute, with a wheel of 52 teeth fixed on it, which is driven by 
a wheel with 60 teeth fixed on the lying-shaft; what number of 
revolutions will the lying-shaft make a minute ? 

96.923 revols. a min. of cross or upright-shaft. 
52 teeth of wheel fixed on shaft. 



193846 
484615 

Teeth oH 

wheel on V 60)5039.996(84 nearly, revolutions of lying-shaft, 
lying shft. J 480 

239 

240 — nearly. 



If a drum 18 inches diameter be fixed on a shaft making 
96.923 revolutions a minute; what number of revolutions will 
the main cylinder of a carding-engine make, with a pulley fixed 
on the cylinder end 15 inches diameter, and driven by a strap 
from the drum 18 inches diameter? 

96.923 revols. a min. of shaft. 
18 inches diam. of drum. 



775384 
96923 



To^^X ' PUll6y } 15)1744.614(116.3 revel, of , 
J ' J 15 cylinder a mm 



mam 



24 
15 

94 

90 

46 
45 

1 

Required the diameter of a pulley to make 116,3 revolutions 



24 SPEED OP SHAFTS. 

a minute; the drum fixed on the shaft being 18 inches diameter, 
making 96.923 revolutions a minute: — 

96.923 revolutions of shaft a minute. 
18 inches diameter of drum. 



775384 
96923 



Kevols. required 116.3)1744.614(15 in. diam. of pulley required. 



5816 
5815 



N. B. — The speed of any piece of machinery may be ascertained, 
according to the foregoing Rules and Examples. 

The speed of a counter-shaft is required, the following parti- 
culars being given : — 

First shaft 96 revolutions a minute. — Drum on said shaft 18 
inches diameter. — Drum on second shaft 14 inches diameter. 
— Drum on the second shaft for driving the third shaft 10 
inches diameter. — Drum on the third shaft 9 inches diameter. 

Drum on 2d shaft 14 inches diameter. 
Drum on 3d shaft 9 inches diameter. 



126 divisor. 



96 revolutions of shaft a minute. 

18 inches diameter of drum on this shaft. 



768 
96 



1728 

10 inches diameter of drum on 2d shaft. 



17280 



SPEED OF SHAFTS — MIXING COTTON. 25 

126)17280(137.14 revols. of counter-shaft a min. 
126 



468 
378 



900 
882 

180 
126 

540 
504 



MIXING COTTON. 

On account of the many varieties and variations even of the 
same kinds of cotton, it will be found best to mix a number of 
bales or bags together ; arranging them properly in the place 
appropriated for the purpose, which done, proceed to throw 
abroad one bale or bag, covering as much surface as convenience 
will allow, according to the number intended to be mixed, and 
proceed till the last is thrown on your stock, treading it well 
down as you proceed. When wanted for use, rake it down with 
a rake, similar to a garden rake, regularly from the top to the 
bottom ; this process will be found not only to mix it regularly, 
but will open the cotton considerably, which is very essential, 
prior to being put through the first preparatory piece of ma- 
chinery. 

In all cases it is best to mix as great a number of bales or 
bags of cotton as can be done conveniently ; because, whenever 
there is a fresh mixing of cotton, it is almost sure to require an 
alteration in some of the machinery, as it seldom happens that 
the new mixing will produce the same weight of roving or yarn. 
3 



26 MACHINERY — WILLOW. 



MACHINERY. 

In treating on machinery, the rules and examples will be laid 
down in the most easy, plain, and simple manner, so that per- 
sons possessing only a knowledge of the fundamental rules of 
arithmetic, will be able to comprehend them : and by following 
the rules, examples, and illustrations laid down, they will be able 
to acquire every qualification requisite, so far as regards calcula- 
tions, for persons filling the important situations of managers or 
overlookers in any or every department of cotton manufacturing. 

In the succeeding calculations, all common fractions, as far as 
possible, are omitted, and decimal fractions used. A knowledge 
of decimals may be easily obtained from almost any work on 
Arithmetic; but the best for the mechanic is the Practical Model 
Calculator, by the editor of this work, Oliver Byrne. 

WILLOW. 

Willows are generally used for opening the cotton, and taking 
out the heavy dirt. They are of various constructions. The one 
of which the following are the particulars, is of recent construc- 
tion : — 

A square cylinder measuring 30 inches from angle to angle. 
4 strips, one at each corner, 4 inches by 3J inches. 
4 strips on the top corners, 4 inches by 3J inches. 
8 teeth or pins in each strip on the cylinder, at a regular dis- 
tance from each other. 
7 teeth in each strip on the top, or cover, and set opposite the 

centre of the spaces. 
Distance of teeth 4 inches; length of teeth 4 inches. 
Diameter of teeth at bottom 1 inch,*regularly tapering to § inch. 
Circular iron grate bars, or rods, half inch distant from each 
other. 

The time for the cotton remaining in the willow is governed 
by wheel-work ; one of the wheels has a pin fixed in it, and 
every time it revolves, works upon a spring connected with a 
lever, which opens the lid and discharges the cotton. 

N. B. — It is customary with some to take off the wheels, having 
the lid continually down, consequently, the cotton thrown in 
will only revolve once or twice, before being discharged. 



BLOWING MACHINE. 27 

This system is adopted by the probability of the cotton being 
strung, by being too long detained in the machine. 

If the shaft for driving a willow makes 158.84 revolutions a 
minute, with a drum fixed on it 26 inches diameter, and the 
pulley on the end of willow cylinder be 12 inches diameter ; what 
number of revolutions will the cylinder make a minute ? 

158.84 revolutions of shaft a min. 

26 inches diam. of drum on shaft. 



95304 
31768 

Inches diameter of "| 

pulley on willow- V 12)4129.84 
cylinder end, J 



344.15333 revols. a min. of cylinder. 

BLOWING MACHINE WITH TWO BEATERS. 

Shaft for driving blowing machine 315.374 revolutions a min. 
Drum on said shaft 45.5 inches diameter. Pulley on beater ends 
10 inches diameter. 

315.374 revolutions of shaft a min. 
45.5 inches diam. of drum on shaft. 



Inches diameter of 
pulley on beaters, 



1576870 
1576870 
1261496 

10)14349.5170 

1434.9517 revols. of beater at blowing 
machine a minute. 



If a pulley 4.75 inches diameter be fixed on the end of a 
beater, making 1535 revolutions a minute; what number of 
revolutions a minute will a shaft make, with a pulley fixed on it 
31 inches diameter, and driven by a strap from the pulley 4.75 
inches diameter ? 



28 BLOWING MACHINE. 

1435 revolutions of beater a minute. 
4.75 in. diam. of puL on beater end. 

7175 

10045 

5740 

Inches diameter of ^ 

pulley on under- > 31)6816.25(219,879 revols. of shaft a min, 
shaft, j 62 

61 
31 



306 

279 



272 
248 

245 
217 



280 
279 



If a wheel with 14 teeth be fixed on the end of the shaft at 
Mowing machine, making 219.879 revolutions a minute ; what 
number of revolutions a minute will a shaft make with a wheel of 
88 teeth, fixed on the end, and driven by a wheel of 14 teeth ? 

219.879 revolutions of given shaft a min. 
14 teeth wheel on end of shaft 



879516 
219879 

3078,306 



BLOWING MACHINE. 29 

^ ee r t V f h ^ eelon } 88)3078.306(34.98 revols. of geering- shaft 
' 264 a minute. 



438 
352 
& 

863 
792 

710 

704 

6 

If a wheel with 35 teeth be fixed on the other end of geering- 
shaft, working into wheel 35 teeth on bottom of bevil-shaft, and 
a wheel 35 teeth on the top of bevil-shaft, be working into a 
wheel 60 teeth on the end of creeper, or delivering-roller ; what 
revolutions will the creeper, or delivering-roller make a minute ? 

34.98 revols. of geering-shaft a min. 
35 teeth wheel on top of bevil-shaft. 



17490 
10494 

Teeth of wheel on") 

end of creeper- V 60)1224.30 

roller, J 

20.405 revols. of creeper, or delivering- 
roller, a minute. 

IT, B. — The 35 teeth wheels on end of geering-shaft, and bottom 
of bevil-shaft are omitted, on account of their being the same 
as carrying, or connecting wheels only. 

If a wheel of 18 teeth be fixed on creeper, or delivering-roller, 
making 20.405 revolutions a minute, working into a wheel on 
stud with 40 teeth, which works into a wheel of 64 teeth on 
another stud, which works into wheel of 96 teeth on the front, 
or second wire cylinder end; what number of revolutions will 
the cylinder make a minute? 



30 BLOWING MACHINE. 

iV. B. — All the intermediate wheels between the creeper-roller and 
wheel on wire cylinder end are omitted in the operation, being 
only carrying, or connecting wheels, which, if made use of, 
must be considered as both driving and driven- wheels. 

20.405 revols. of creeper-roller a min. 
18 teeth, wheel on end of roller. 



163240 
20405 



S^Ldttd: n } 9 ^p90(3.826nea r l r evol, 2d wire 
J ? } 288 cylinder a mmute. 



792 
768 

249 
192 



570 

576 — nearly. 

If a wheel with 52 teeth he fixed on the end of geering-shaft, 
making 34.98 revolutions a minute, working into a wheel of 52 
teeth (a shaft which is the length of the machine, for propelling 
the shafts of the feed-rollers) ; on the lying-shaft is a wheel with 
50 teeth working into a wheel on the bottom of upright-shaft 
40 teeth, and a wheel with 39 teeth on the top of upright-shaft, 
working into a wheel 82 teeth on the end of the feed-rollers; 
what number of revolutions will the feed-rollers make ? 

JV. B. — The first two wheels, 52 teeth each, are omitted, being only 
carrying or connecting wheels. 

When there are more than one driving and driven-wheels, 
multiply the revolutions a minute of your given shaft by the driv- 
ing-wheels respectively for a dividend, and your driven-wheels 
(only) together for a divisor, and the quotient will be the revolu- 
tions a minute required. 



BLOWING MACHINE. 31 

34.98 revolutions of given shaft a minute. 
50 teeth wheel first driver. 



1749.00 

39 teeth wheel top of upright-shaft working 
into wheel 82 teeth on roller end. 



15741 

5247 



68211 dividend. 



40 teeth wheel on bottom of upright-shaft. 
82 teeth wheel on feed-roller end. 



3280 divisor. 

3280)68211(20.796 revols. a min. of 2d feed-roller. 
6560 



26110 

22960 

31500 
29520 



19800 
19680 

120 

If a wheel with 12 teeth be fixed on the end of the feed-rollers, 
making 20.793 revolutions a minute, works into a stud-wheel 26 
teeth, which works into wheel 26 teeth on the first creeper-roller 
end; what number of revolutions a minute will the first creeper- 
roller make? 

20.793 revols. of 2d feed-roller a min. 
12 teeth in wheel on feed-roller. 



IsTcr f 7 heel ° n } 26 ) 2 49.516(9.6 revols. of 1st creeper-roller 
ee P er > ' 234 a minute. 



155 

156 — nearly. 



32 BLOWING MACHINE. 

If a wheel with 16 teeth be fixed on the first creeper-roller, 
making 9.6 revolutions a minute, works into a stud-wheel 96 
teeth (carrier), which works into wheel of 96 teeth on first wire 
cylinder end ; what number of revolutions will the first wire cylin- 
der make a minute? 

9.6 revols. of first creeper-roller a min. 
16 teeth-wheel fixed on first creeper-roller. 



576 
96 



Teeth of wheel 1 96 ) 153>6 / 1#6 revolg< of lst ire L ; t 
on 1st wire cyl. J qq 



576 
576 



If a wheel with 40 teeth be fixed on a lying-shaft, making 
34.98 revolutions a minute, works into a wheel 50 teeth on the 
bottom of an upright- shaft, and a wheel 40 teeth fixed on the 
top of upright-shaft works into wheel 82 teeth on end of feed- 
rollers ; what number of revolutions will the first feed-roller make 
a minute ? 

Wheel on bottom of upright-shaft 50 teeth. 
Wheel on lst feed-roller end 82 teeth. 



4100 divisor. 



34.98 revolutions of lying-shaft a minute. 
40 teeth wheel on lying-shaft. 

1399.20 

40 teeth wheel on top of upright-shaft. 



4100)55968.00(13.65 revolutions of 1st feed-roller a min. 
41 

149 
123 

■ 208 

266 205 

246 ■ 

„_ 3 



BLOWING MACHINE. 33 

If a wheel with 12 teeth fixed on the end of feed-rollers, making 
13.65 revolutions a minute, works into a wheel of 26 teeth on 
feed-cloth-roller ; what number of revolutions a minute will the 
feed-cloth-roller make? 

13.65 revols. of feed-roller a min. 
12 teeth wheel on end. 



Teeth of wheel on end of l 26)163i80(6#3 reyolg . of feed . cloth . 
feed-cloth-roller, / \^ roller a minute. 



78 

78 

If the feed-cloth-roller be 3 inches diameter, making 6.3 revo- 
lutions a minute; how many inches will the feed-cloth traverse? 
6.3 revols. of feed-cloth-roller a minute. 
3 inches diameter of feed-cloth-roller. 



18.9 
3.1416 circumference when the diam. is 1. 



1134 

189 
756 
189 

567 



59.37624 inches feed-cloth traverses a min. 

If the first creeper-roller be 3.5 inches diameter, making 9.6 
revolutions a minute; how many inches will it traverse? 

3.1416 circumference when the diameter is 1. 
3.5 diameter of creeper-roller. 



157080 
94248 



10.99560 inches circumference of creeper-roller. 



6597360 
9896040 



105.557760 inches first creeper-roller traverses a min. 



34 BLOWING MACHINE. 

If the second feed-roller be 1.5 inch diameter, making 20.793 
revolutions a minute ; how many inches will it traverse ? 

3.1416 circumference when the diameter is 1. 
1.5 diameter of feed-roller. 



157080 
31416 



4.71240 inches circumference of feed-roller. 

20.793 



141372 
424116 

329868 
942480 

97.9849332, or nearly 98 inches feed-roller traverses 
a minute. 

If the second creeper, or delivering-roller, be 3.5 inches di- 
ameter, making 20.405 revolutions a minute; how many inches 
will it traverse? 

3.1416 circumference when the diameter is 1. 
3.5 inches diameter of second creeper, or de- 

livering-r oiler. 

157080 
94248 



10.99560 inches circumference of second creeper, or 
20.405 delivering-rollers. 

549780 
4398240 
2199120 



224.3652180 inches creeper, or delivering-roller, traverses 

a minute. 

N. B. — The draught of any 'piece of machinery may be ascer- 
tained by dividing the distances traversed, into each other, as 
ivill appear in a future part of this work. 



DIMENSIONS AND MOTIONS OF A DOUBLE BLOWING MACHINE. 35 



DIMENSIONS AND MOTIONS OF A DOUBLE BLOWING MACHINE. 

Beaters make 1435 revolutions a minute. 

Feed-cloth-roller makes 6.3 revolutions a minute. 

First feed-roller makes 13.65 revolutions a minute. 

First creeper-roller makes 9.6 revolutions a minute. 

First wire cylinder makes 1.6 revolutions a minute. 

Second feed-roller makes 20.8 revolutions a minute. 

Second creeper, or delivering-roller, in the front of machine, 

makes 20.405 revolutions a minute. 
Second wire cylinder makes 4.888 revolutions a minute. 
Distance of grate-bars from each other \ an inch. 
Distance of grate-bars from beaters 1J to J an inch. 
Diameter of beaters 18 inches. 
Diameter of feed-cloth-rollers 3 inches. 
Diameter of iron-feed-rollers 1J inch. 
Diameter of plain iron-rollers 2 inches. 
Diameter of creeper-rollers 3J inches. 
Diameter of wire cylinder 22 inches. 

N. B. — The rollers not named a second time are of the same di- 
mensions as those above. 

Feed-cloth-roller traverses 59.37624 inches a minute. 
First creeper-roller traverses 105.55776 inches a minute. 
Second feed-roller traverses 98 inches a minute — nearly. 
Second creeper, or delivering-roller, traverses 224.365218 inches 
a minute. 

N.B. — The above particulars will materially differ from some 
blowing machines, but the particulars of any machine may be 
found by following the examples and illustrations laid down. 

LAP MACHINE. 

It has become very general of late years to have two lap ma- 
chines, in place of a blowing machine and a lap machine, and 
where it is the case, two or three laps from the first machine are 
put up at the second, which has a great tendency to equalize the 
lap, and produce more even carding; however, the following are 
the particulars where only a certain weight is fed on a given 
length of the feed-cloth without any doubling, but there will be 
little diiference in the machine further than the difference at the 
feeding parts, or in the draughts of the machine. 



36 LAP MACHINE. 

If the shaft for driving a lap machine makes 315.3747 revo- 
lutions a minute, the drum on said shaft 40.5 inches diameter, 
and the pulley on the beater end 11.25 inches diameter; how 
many revolutions will the beater make a minute? 

315.3747 revolutions of shaft a minute. 
40.5 



15768735 
126149880 



of Ddlev™ ' } n - 25 ) 12 772.67535(1135.3489 revols. of beater a 
' P ^ ? J 1125 minute. 

1522 
1125 



3976 
3375 



6017 
5625 

3925 
3375 



5503 
4500 

10035 
9000 

10350 
10125 

225 

If a pulley 4.75 inches diameter be fixed on the end of a beater 
making 1135.3489 revolutions a minute ; what revolutions a 
minute will a shaft make with a pulley fixed on it 31.5 inches 
diameter, and driven by a strap from the pulley 4.75 inches 
diameter ? 



LAP MACHINE. 37 

1135.3489 revolutions of beater a min. 

4.75 in. diam. of pulley on beater 
end. 



56767445 
79474423 
45413956 



^lle^onshaff \ 31 - 5 ) 5392 : 9 °7275(171.2 revols. of shaft work- 
^ 315 ing geering a minute. 



2242 
2205 



379 
815 

640 
630 

10 

If a wheel 14 teeth be fixed on shaft making 171.2 revolu* 
tions a minute, and works into a carrying-wheel with 30 teeth, 
which drives a wheel 88 teeth on geering-shaft ; what number of 
revolutions a minute will the geering-shaft make. 

171.2 revols. of shaft a min. working geering* 
14 teeth wheel fixed on said shaft. 



6848 
1712 
Teeth of wheel 



on geering- > 88)2396.8(27.236 revols. a minute of geering- 
shaft, ) 176 shaft. 

636 
616 

208 
176 

' . 560 

320 528 

264 — - 

*— 32 



38 LAP MACHINE. 

If a wheel with 16 teeth be fixed on a shaft making 27.236 
revolutions a minute, works into a wheel 88 teeth on the end of 
lap-roller; how many revolutions will the lap-roller make a 
minute ? 

27.236 revolutions of shaft a minute. 
16 teeth wheel on said shaft. 



163416 

27236 



Teeth of wheel on 



la -roller \ 88 ) 435 ^76(4.952 revols. of lap-roller a min. 



352 

837 

792 



457 
440 



176 
176 



JV. B.— There is a wheel of 30 teeth fixed on the first tap-roller, 
which works into a wheel 20 teeth on stud, which drives a 
ivheel 30 teeth on the second lap-roller, consequently it will be 
the same speed as the first. 

If a wheel 22 teeth fixed on geering-shaft ? make 27.236 revo- 
lutions a minute, works into a wheel 88 teeth on front iron-roller; 
what number of revolutions will the front iron-roller make a 
minute? 

27.236 revols. of geering-shaft a min, 
22 teeth wheel on geering-shaft. 



54472 
54472 



Teeth of wheel on ) §8)599.192(6,809 revolutions of front iron- 
front iron-roller. S coo n ■ *. 
5 } 528 roller a minute. 

711 

704 

792 

792 



LAP MACHINE. 39 

If a wheel of 20 teeth fixed on the front iron-roller, making 

6.809 revolutions a minute, works into a wheel of 19 teeth on 

stud, which works into a wheel of 19 teeth on creeper-roller; 

what number of revolutions will the creeper-roller make a minute ? 

6.809 revolutions of iron-rollers a min. 

20 teeth wheel fixed on iron-rollers. 



Teeth of wheel on) i 9 yi36.l80(7.167 revol. of creeper-roller a 
creeper-roller, / ^ minute> 



31 
19 

128 
114 

140 
133 



If a wheel of 18 teeth fixed on the end of creeper-roller, making 

7.167 revolutions a minute, works into a wheel with 64 teeth on 

stud, which works into a wheel of 96 teeth on wire cylinder end; 

what number of revolutions will the wire cylinder make a minute? 

7.167 revols. of creeper-roller a min. 

18 teeth wheel fixed on creeper-roller, 



57336 

7167 



w^^nder 1011 \ 96 ) 129 - 006 ( 1 - 3438 revols. of wire cyl. a min, 



330 

288 

420 

384 



— 780 
366 768 
288 

— 12 



40 LAP MACHINE. 

If a wheel with 36 teeth, fixed on the end of the creeper-roller, 
making 7.167 revolutions a minute, works into a wheel with 36 
teeth on feed-roller shaft, and on the other end of feed-roller 
shaft is a wheel with 46 teeth, which works into a wheel with 30 
teeth on feed-roller end ; what number of revolutions will the 
feed-rollers make a minute ? 

7.167 revols. of creeper-roller a min. 
46 teeth on end of feed-roller shaft. 



43002 

28668 



Teeth of wheel on 



;r~T „ VTilcc " Uil 30)329.682 
ieed-roller, ) ' 



10.9894 nearly 11 revolutions of feed- 
rollers a minute. 

N. B.—The two 36 teeth wheels are not noticed, the one being a 
driver, and the other driven. 

If a wheel with 12 teeth fixed on feed-rollers, making 10.9894 
revolutions a minute, works into a stud-wheel of 26 teeth, work- 
ing into wheel of 26 teeth on feed-cloth-roller end; what number 
of revolutions will the feed-cloth-roller make a minute? 

10.9894 revols. of feed-roller a min. 
12 teeth wheel on feed-rollers. 



J eG i h i °L ^\T l ° n \ 26)131.8728(5.072 revols. of feed-cloth- 
leed-cloth-roller, j \ OA v „ . , 

? J 130 roller a minute. 



187 
182 

52 
52 

What number of inches will the feed-cloth traverse a minute, 
if the diameter of feed-cloth-roller be 3 inches.) making 5.072 
revolutions a minute ? 



LAP MACHINE. 41 

N, B. — To find the circumference of wheels , drums, pulleys, roll- 
ers, $c, multiply the diameters by 3.1416, which is equal to the 
circumference when the diameter is 1. 

5.072 revols. of feed-cloth- roller a min. 
3 inches diameter of feed-cloth-rol. 



15.216 
3.1416 

91296 
15216 
60864 
15216 
45648 

47.8025856 being rather more than 47f in. 
feed-cloth traverses a minute. 

If the feed-rollers of lap machine be 1 J inch diameter, making 
10.9894 revolutions a minute; what number of inches will they 
traverse a minute? 

10.9894 revolutions of feed-rollers a min. 
1.5 inch diameter of feed-rollers. 



549470 

109894 



16.48410 

3.1416 circumference when the diam. is 1. 



989046 
164841 
659364 
164841 
494523 



51.78644856 inches feed-rols. traverse a min. 

What is the draught between feed-cloth and feed-rollers, from 
the two preceding examples? 
4 



42 LAP MACHINE. 

Inches feed-cloth traverses. Inches feed- rollers traverse. 

47.8025856)51.78644856(1.083 inch draught be- 
478025856 tween feed-cloth 

. an( j feed-roller. 



3983862960 
3824206848 

1596561120 
1434077568 



162483552 

If the creeper-roller at lap machine be 3J inches diameter, 
making 7.167 revolutions a minute ; what number of inches will 
it traverse in a minute ? 

7.167 revolutions of creeper-roller a minute. 
3.5 inches diameter of creeper-roller. 



35835 
21501 



25.0845 
3.1416 equal to circumference when diam. is 1, 



1505070 

250845 
1003380 
250845 
752535 

78.80546520 inches creeper traverses a minute. 

Required the draught between the feed-rollers and the creeper ; 
the feed-rollers traversing 51.78644856 inches a minute, and the 
creeper the same as in the preceding example. 



LAP MACHINE. 43 

Inches feed-rollers traverse. Inches the creeper traverses. 

51.78644856)78.80546520(1.5217 draught between 
5178644856 feed-roller and 

creeper-rollers. 



27019016640 

25893224280 

11257923600 

10357289712 

9006338880 
5178644856 

38276940240 
36250513992 

2026426248 



If the iron-roller in front of lap machine be 3]-| inches diame- 
ter, making 6.809 revolutions a minute; what number of inches 
will it traverse a minute? 

(4)15.00 decimal of if = .9375 

16 1 

( 4)3.75 

- — inches. 6.809 revols. of iron-rol. a min. 

.9375 therefore= 3{ §^=3.9375 inches diam. on iron-rol. 



34045 
47663 

20427 
61281 

20427 

26.8104375 

3.1416 circum. when diam. is 1. 



1608626250 
2681043^5 
1072417500 
268104375 
804313125 



84.22767045000 inches, or 84J inches 
nearly, iron-roller front of lap machine traverses a minute. 



44 LAP MACHINE. 

Required the draught between creeper-roller and iron-roller, 
from the preceding examples. 
Inches. Inches. 

78.8)84.22767(1.068 draught between creeper-roller 
788 and iron-roller at lap machine. 



5427 

4728 

6927 



6996 6304 
6304 



623 



IV. B. — It is not practically necessary or requisite to carry any 
examples to more than 3 or 4 decimal figures, however they may 
occur in multiplying ; but they may be used if thought proper 
in dividi7ig. 

If the lap-roller be 6J inches diameter, making 4.952 revolu- 
tions a minute; how many inches will it traverse a minute? 
4.952 revolutions of lap-roller a minute. 
6.5 inches diameter of lap-roller. 

24760 
29712 



32.1880 
3.1416 

193128 

32188 
128752 
32188 
96564 

101.1218208 inches lap-roller traverses a minute. 

Required the draught between the iron-roller and the lap-roller, 
from the preceding examples. 

Inches. Inches lap-roller traverses a minute. 
84.2276)101.1218208(1.2 draught between iron-roller and 
842276 lap-roller, 

1689422 
1684552 

4870 



LAP MACHINE. 45 

The total draught at the lap machine may be ascertained by 
multiplying the different draughts into each other : 

OR, 

By multiplying all the driving-wheels together, beginning at 
the wheels driving the lap-roller, and taking them respectively 
(except the driving and driven-wheels, which, being of the same 
number of teeth, are omitted) to the feed-cloth-roller, the pro- 
duct of which must be multiplied by the diameter of the feed- 
cloth-roller, for a divisor, and all the driven-wheels multiplied in 
the same manner, the products of which must be multiplied by 
the diameter of the lap-roller for a dividend, and the quotient 
will be the draught, as in the following examples: — 

Draught between feed-cloth and feed-rollers 1.08. 
Draught between feed-roller and creeper-roller 1.52. 
Draught between creeper-roller and iron-roller 1.068. 
Draught between iron-roller and lap-roller 1.2. 

1.08 draught between feed-cloth and feed-rollers. 
1.52 draught between feed-roller and creeper-roller,, 



216 

540 
108 



1.6416 

1.0688 draught between creeper-roller and iron-roller 



131328 
131328 

98496 
164160 

1.75454208 

1.2 draught between iron-roller and lap-roller. 



350908416 
175454208 



2.105450496 total draught at lap machine. 

THE SAME EXAMPLE AS LAST — BY WHEELS. 

The first driven-wheel on lap-roller is 88 teeth, working into a 
wheel 16 teeth on the end of geering-shaft ; then on the other 



46 LAP MACHINE. 

end of geering-shaft there is a wheel with 22 teeth, working into 
a wheel with 88 teeth on iron-roller ; on the other end of iron- 
roller a wheel with 20 teeth works into a wheel with 20 teeth on 
the top-roller, which works into a wheel with 20 teeth on a stud, 
which works into a wheel with 19 teeth on the creeper-roller end; 
on the other end of creeper-roller there is a wheel with 36 teeth, 
working into a wheel with 36 teeth on the end of the feed-roller- 
shaft; on the other end of the feed-roller-shaft there is a wheel 
with 46 teeth working into a wheel with 30 teeth on the end of 
the feed-roller; on the other end of the feed-roller there is a 
wheel with 12 teeth working into a wheel with 26 teeth on a stud, 
which works into a wheel with 26 teeth on the end of the feed- 
cloth-roller ; the lap-roller is 6 J inches diameter, and the feed- 
cloth-roller 3 inches diameter; what is the draught at lap 
machine ? 

DRIVING-WHEELS. 

88 teeth wheel on lap-roller. 
22 teeth wheel on geering-shaft. 



176 
176 

1936 

20 teeth wheel 


on iron-roller., 
on feed-shaft. 

on feed-roller, 
eter of feed-cloth- 




38720 

46 teeth wheel 




232320 

154880 




1781120 

12 teeth wheel 




21373440 

3 inches diam 


roller. 



64120320 divisor. 

iV. B. — The carrying, or connecting wheels, and driving and 
driven-wheels working together, where they contain the same 
number of teeth, are omitted, as will be found in the preceding 
and following examples :—- 



LAP MACHINE. 47 

DRIVEN-WHEELS. 

16 teeth wheel on geering-shaft. 
88 teeth wheel on iron-roller. 



128 
128 

1408 

19 teeth whe^el on creeper-roller. 


12672 
1408 




26752 

30 teeth wheel 


on feed-roller. 


802560 

26 teeth wheel 


on feed-cloth-roller. 


4815360 
1605120 




20866560 

6.5 diameter of 


lap-roller. 


104332800 
125199360 




135632640.0 dividend. 





Divisor. 

64120320)135632640(2.115 draught at lap machine. 
128240640 



73920000 
64120320 

97996800 
64120320 



338764800 
320601600 

18163200 



48 CARDING-ENGINE. 

N. B. — The small difference between the last two examples is in 
the method of working, arising from the decimal parts ; how- 
ever, working draughts by wheels, as in the last example, is the 
surest way where great accuracy {which is indispensable), is 
required. 

The following are the particulars of a lap machine, where 
there are no doublings : — 

Beater makes 1135.348 revolutions a minute. 
Feed-cloth-roller makes 5.072 revolutions a minute. 
Feed-rollers make 10.9894 revolutions a minute. 
Creeper-roller makes 7.167 revolutions a minute. 
Iron-rollers make 6.809 revolutions a minute. 
Lap-rollers make 4.952 revolutions a minute. 

Distance of grate-bars from each other \ an inch. 
Distance of grate from beater 1 inch. 
Diameter of beater 18 inches. 
Diameter of feed-cloth-roller 3 inches. 
Diameter of feed-rollers \\ inch. 
' Diameter of creeper-roller 3J inches. 
Diameter of iron-rollers 3{f inches. 
Diameter of lap-rollers 6J inches. 

Feed-cloth-roller traverses 47.7025856 inches a minute- 
Feed-rollers traverse 51.78644856 inches a minute. 
Creeper-rollers traverse 78.8054652 inches a minute. 
Iron-rollers traverse 84.2276704 inches a minute. 
Lap-rollers traverse 101.12182808 inches a minute. 

Draught between feed-cloth and feed-rollers 1.108. 
Draught between feed-rollers and creeper 1.52. 
Draught between creeper and iron-rollers 1.0688. 
Draught between iron-rollers and lap-rollers 1.2. 

Total draught at lap machine 2.115. 

CARDING-ENGINE. 

Carding-engines are of various constructions, but the construc- 
tion of machinery will make no difference in the system of cal- 
culation, as all the various speeds, &c, are ascertained from that 
part which first receives motion, which is without exception the 
main cylinder. 



CARDING-ENGINE. 49 

The opinions of persons connected with cotton carding are dif- 
ferent; however, all nearly agree in the most essential points, 
that is, in having the cards true and sharpened to a diamond 
point, and whether worked with rollers, rollers and clearers, 
rollers clearers and part flats, or all flats, to have the wire set 
near as possible, so as not to touch each other, the first 3 or 4 
flats set rather more on the heel, or back of card, for the purpose 
of detaining the heavy dirt. Some kinds of cotton require con- 
siderably more carding than others ; however, it may be observed, 
that the less cotton is carded the better, so that the dirt is taken 
out, and the fibres laid straight, after which, the cotton by being 
continued in the cards is only weakened, consequently the yarns 
will be weakened in proportion, which must appear reasonable to 
any practical person. 

If a shaft make 95.3057 revolutions a minute, with a drum 
fixed on it 16 inches diameter; what number of revolutions a 
minute will the main cylinder of a carding-engine make, with a 
pulley fixed on it 14 inches diameter, and driven with a strap 
from the drum 16 inches diameter? 

95.3057 revolutions of shaft a minute. 
16 inches diameter of drum. 



5718342 

953057 



^lhT dlam ' ° f ( 14 ) 1524 - 8912 ( 109revols - ofmainc y lindera 

P ^' * 14 minute. 



124 

126 — nearly. 

If the main cylinder of a carding-engine makes 108.92 revo- 
lutions a minute, with a wheel on its axis of 22 teeth, working 
into a wheel of 140 teeth on stud — on same stud there is a wheel 
of 32 teeth, working into a wheel of 130 teeth on a stud, which 
drives a wheel of 130 teeth on end of doffer-cylinder — what num- 
ber of revolutions will the main cylinder make for the doffer- 
cylinder one, and what number of revolutions will the doffer- 
cylinder make a minute ? 



50 CARDING-ENGINE. 



140 teeth wheel on stud. 
130 teeth wheel on doffer-cylinder end. 



4200 
140 



18200 divisor. 



108.92 revolutions of main cylinder a min. 
22 teeth wheel on axis of cylinder. 



21784 

21784 



2396.24 

32 teeth wheel on stud. 



479248 

718872 



18200)76679.68(4.213 revols. of doffer-cylinder a min. 

72800 



38796 
36400 



23968 
18200 

57680 
54600 

3080 

The revolutions of the main cylinder for the doffer-cylinder 
one, will be found by dividing the revolutions of the main cylin- 
der by the revolutions of the doffer-cylinder. 



CARDING-ENGINE. 51 

Revols. of doffer-cyl. 4.213)108.92(25.85 revols. of main cyl. for 

8426 doffer 1. 



24660 
21065 

35950 
33704 



22460 
21065 

1395 

The number of revolutions the main cylinder makes for the 
doffer-cylinder one, will be found by multiplying the driving- 
wheels together for a divisor, and the driven-wheels together for 
a dividend, as in the following example: — 

DRIVING-WHEELS. 

Wheel on cylinder end 22 teeth. 
Wheel on stud 32 teeth. 



704 divisor. 

DRIVEN-WHEELS. 

Wheel on stud 140 teeth. 
Wheel on doffer-cylinder 130 teeth. 



4200 
140 



18200 dividend. 
704)18200(25.85 revols. main cylinder makes for 
1408 doffer-cylinder 1. 

* 4120 
3520 

■ — 3680 

6000 3520 

5632 . — 

— 160 



52 CARDING-ENGINE. 

What will the main cylinder of a carding-engine traverse a min. 
if it makes 108.92 revolutions, and its diameter be 37 inches? 
108.92 revols. of main cyl. a minute. 
37 inches diam. of main cylinder. 

76244 
32676 



4030.04 
3.1416 circum. when the diam. is 1. 



2418024 
403004 
1612016 
403004 
1209012 



1 foot = 12 in. )12660. 773664 inches main cyl. trav. a minute. 



1 yard == 3 feet)1055. 064472 feet main cyl. trav. a minute. 

351.688157333 yards main cyl. trav. a min. 

What surface will the doffer-cyl. of a carding-engine traverse 

a minute, if it makes 4.213 revolutions, and is 18 inches diameter? 

4.213 revolutions of doffer-cyl. a minute. 

18 inches diameter of doffer-cylinder. 



33704 
4213 



75.834 

3.1416 circumference when the diam. is 1. 



455004 

75834 
303336 

75834 

227502 



1 foot = 12 in.)238. 2400944 inches doffer-cyl. trav. a minute. 
1 yard = 3 feet )19.8533412 feet doffer-cyl. trav. a minute. 
6.6177804 yards doffer-cyl. trav. a minute. 



CARDING-ENGINE. 53 

How many feet of fillet, 2 inches wide, will it require to cover 
a doffer-cylinder 18 inches diameter, and 36 inches wide ? 

3.1416 circumference when the diam. is 1. 
18 inches diameter of doffer-cylinder. 



251328 
31416 



56.5488 

36 inches width of doffer-cylinder. 



3392928 
1696464 



of C fiDet Wldth \ 2 ) 2035 - 7568 inches area of doffer-cylinder. 
1 foot = 12 in.)1017.8784 inches of fillet required for cyl. 



84.8232 or nearly 85 feet of fillet required 
for cylinder. 

iV". B. — By taking the taper off one end of the fillet, and putting 
it to the other end, nearly 5 feet of fillet will be saved; conse- 
quently 80 feet of the above fillet will be sufficient to cover a 
cylinder of the above dimensions. 

Whatever the width of the fillet is, divide the number of inches 
in the area of the cylinder, by the width of the fillet, and the 
quotient will be the number of inches required to cover the cylin- 
der ; then deduct the inches in the circumference of the cylinder 
from the quotient, and the remainder will be the net length of 
fillet required. 

N. B. — The circumference of the cylinder must only be deducted 
when the taper end is cut off the beginning of the fillet, and is 
intended to be put on at the other end. 

How many feet of 1J inch fillet will be required to cover a 
cylinder 18 inches diameter, and 36 inches wide? 



54 CARDING-ENGINE. 



3.1416 equal to circum. when diam. is 1. 
18 inches diameter of cylinder. 



251328 
31416 



56.5488 circumference of cylinder. 
36 inches width of cylinder. 

3392928 
1696464 



2035.7568 
Deduct 56.5488 circumference of cylinder. 



Jf C fillet Wldth } L5)19 7 9 - 2080 ( 1319 - 4 72 inches of fillet required 
' 15 to cover the cylinder. 



47 
45 



Or, 

29 1 ft. ^12 in.)1319.472 inches. 
15 

lyd. = 3feet)109.956 or nearly 110 ft. 



142 



135 36.652 yds., nearly 36^ 
yards 

70 

60 



108 
105 



30 

30 

Required the speed of the feed-rollers of a carding-engine, 
from the following particulars: — 

Revolutions of doffer-cylinder a minute 4.213. 

Wheel on doffer-cylinder end, driving feed-roller-shaft 28 teeth. 

Wheel on feed-roller-shaft (doffer end) 28 teeth. 

Wheel on feed-roller-shaft, driving feed-rollers 13 teeth. 

Wheel on feed-roller end 128 teeth. 



CARDING-ENGINE. 55 

N. B. — The wheels 28 teeth on the doffer-cylinder end, and feed- 
roller-shaft, may be omitted, the one being a driving and the 
other a driven-ivheel. 

4.213 revols. of doffer-cyl. a minute. 
13 teeth wheel on feed-roller shaft. 



12639 
4213 



.ro°lLT- h shaft n I 128 ) 54 - 769 (- 42 ? 8 revols - of feed-rols. a 



356 
256 

1009 

896 



1130 
1024 

106 

If the diameter of the feed-rollers be 1J inches, making .4278 
revolutions a minute ; how many inches will the feed-rollers tra- 
verse ? 

.4278 revolutions of feed-rollers a min. 
1.5 inches diameter of feed-rollers. 



21390 

4278 



.64170 

3.1416 circumference when diameter is 1. 



385020 

64170 
256680 
64170 
192510 

2.015964730 or 2^ inches nearly feed-rollers 
traverse a minute. 



56 CARDING -ENGINE. 

i 

What length of lap will be required to supply a carding-engine 
1 day, allowing it to work 10 hours (2 hours being allowed for 
stripping, grinding, &c), if the feed-rollers traverse 2.01596472 
inches a minute? 

2.01596472 inches feed-rols. traverse a minute. 
60 minutes = 1 hour. 



120.95788320 

10 hours = 1 day. 



1209.57883200 inches, or nearly 100 feet 10 
inches a day. 
Required the weight of cotton to supply a carding-engine 1 
day, the feed-rollers of which traverse over a surface equal to 
1209.578832 inches, there being 24 ounces fed on 30 inches of 
feed-cloth at lap machine, and the draught at lap machine being 
2.115. 

oz. cotton. 
Draught at lap machine, 2.115)24.000(11.347517 oz. weight of 30 

2115 inches of lap. 



2850 
2115 



7350 
6345 

10050 

8460 

15900 

14805 

10950 
10575 






3750 
2115 

16350 
14805 

1545 



CARDING-ENGINE. 57 

Feed-cloth at lap mach. 30 in.)1209.578832 in. feed-rols. trav. 



40.3192944 number of feeds. 
11.347517 oz. weight of 30 in. 
of lap. 



2822350608 
403192944 
2015964720 
2822350608 
1612771776 
1209578832 
403192944 
403192944 

4)457.5238786320048 nearly 457J oz., or 

28 T 6 oifos. nearly. 

4)114.3809696580012 

28.5952424145003ft>s. 

OR, 

Multiply the number of inches (say 30), on which 24 ounces 
weight of cotton is fed on the feed-cloth at lap machine, by the 
draught at lap machine, (draught 2.115,) and that sum by the 
number of ounces in lib. for a divisor, and the number of inches 
the feed-rollers traverse in one day, or 10 hours, by the number 
of ounces fed on 30 inches on feed-cloth at lap machine, for a 
dividend, and the quotient will be the pounds weight required to 
supply the engine. 

2.115 draught at the lap machine. 

30 inches length fed on feed-roller. 



63.450 

16 ounces make one pound. 



380700 
63450 



1015.200 divisor. 



58 CARDING-ENGINE. 



1209.578832 inches of lap required a day. 

24 oz. weight fed on 30 inches of feed- 
cloth at lap machine. 

4838315328 
2419157664 



1015.2)29029.891968(28.5952 pounds a day. 

20304 16 ounces= 1 pound. 



87258 35712 

81216 5952 



60429 9.5232 oz. 

50760 4 qrs.=l oz. 



96691 2.0928 qrs. 

91368 



53239 

50760 

24796 
20304 



4492 

JV. B.—-The weight of cotton required to supply a preparation, 
must be according to the number of car ding -engines. The 
weight consumed by one carding-engine, multiplied by the 
number of carding-engines in the preparation, will give the 
iveight of cotton required. 

What number of revolutions will the doffer-cylinder of a card- 
ing-engine make, for the feed-rollers 1, if the wheels on the 
doiFer-cylinder end and feed-roller-shaft be the same ; and on the 
other end of feed-roller-shaft, a wheel with 13 teeth, working 
into a wheel 128 teeth on feed-roller end ? 
Teeth of wheel on feed-shaft, 13)128(9.846 revols. of doffer-cyl. for 

. 117 feed-rollers 1. 



110 




104 


80 




78 


60 


. . 


52 


2 



CARDING-ENGINE. 59 

The speed of the lap-rollers at carding-engine is required from 
the following particulars : — 

Revolutions of feed-rollers a minute, .4278 ; wheel on feed- 
roller end 17 teeth, working into a wheel 84 teeth on stud, which 
works into a wheel 46 teeth on lap-roller. 

.4278 revolutions of feed-rollers. 
17 teeth wheel on feed-rollers. 



29946 

4278 



k ee -roll°e f r Wheel ^ } 46 )7-2726(.1581 revols. of lap-rollers a min. 
r ? J 46 

267 
230 

372 

368 

46 
46 

If the lap-roller makes .1581 revolutions a minute, and be 3| 
inches diameter ; what number of inches will it traverse ? 
.1581x3.75=. 592875x3.1416=1.8625761, or rather more 
than l.JJ inches, lap-roller traverses a minute. 

If the feed-rollers traverse 2.01596472 inches a minute, and 
the lap-rollers 1.862576 inches; what draught is there between 
the feed-rollers and lap-rollers ? 

1.862576 in.)2.01596472(1.082 draught between lap-rollers ? 
1862576 and feed-rollers. 



15338872 
14900608 



4382640 
3725152 

657488 



60 CARDING-ENGINE. 

OR, 

The draught between the feed-rollers and lap-rollers is required 
from the following particulars : — 

Wheel on end of feed-rollers 17 teeth, working into stud-wheel 
84 teeth, which works into wheel 46 teeth on the end of lap- 
rollers ? 

Diameter of feed-rollers, 1J inches. 
Diameter of lap-rollers, 3f inches. 

3.75 inches diameter of lap-rollers. 
17 teeth in wheel on feed-rollers. 



2625 
375 



63.75 divisor. 



1.5 inches diameter of feed-rollers. 
46 teeth wheel on lap-rollers. 

90 
60 



63.75)69.00(1.0823 draught between lap-rollers and 
63.75 feed-rollers. 



52500 
51000 

15000 
12750 



22500 
19125 

3375 

Required the draught between the feed-rollers and lap-rollers ? 
from the following particulars: — 

Revolution of feed-rollers a minute, .4278. 
Revolution of lap-rollers a minute, .1581. 
Diameter of feed-rollers, 1.5 inches. 
Diameter of lap-rollers, 3.75 inches* 



CARDING-ENGINE. 61 

.1581 revolution of lap-rollers a minute. 
3.75 inches diameter of lap-rollers. 



7905 
11067 
4743 



5.92875 divisor. 



.4278 revolution of feed-rollers a minute. 
1.5 inches diameter of feed-rollers. 



21390 

4278 



5.92875)6.41700(1.082 draught between feed-rollers 
592875 and lap-rollers- 

4882500 
4743000 



1395000 
1185750 

209250 



What weight of cotton will be required to supply a carding- 
engine 1 day, or 10 hours, according to the following particu- 
lars? 

Weight fed on 30 inches of feed-cloth at lap machine, 24 ounces* 
Draught at lap machine 2.115. 
Lap-roller traverses 1.862576 inches a minute. 

60 minutes 1 hour. 



111.754560 

10 hours = 1 day. 



1 foot = 12 in.)1117. 545600 inches a day, lap-rol. traverses. 
93.1288 feet a day, lap-roller traverses. 



62 CARDING-ENGINE. 



93.1288 feet of lap required a day. 

24 oz. weight fed on 2J feet, or 30 inches of 
feed-cloth at lap machine. 



3725152 

18625T6 



2235.0912 dividend. 



2.115 draught at lap machine. 

2.5 feet, or 30 in. feed-cloth at lap machine. 



105T5 
4230 



5.2875 

16 ounces — 1 pound. 



317250 

52875 



84.6000 divisor. 



84.6)2235.0912(26 6| weight of cotton required, 
1692 to supply a carding-engine 

1 day, or 10 hours. 

5430 
5076 



354 
16 ounces 1 pound* 



2124 
354 



84.6)5664(6 oz. 
5076 



588 

4 



84.6)2352(2 qrs. 
1692 

66.G 



CARDING-ENGINE. 63 

N, B. — If there had been no draught between the feed-rollers and 
lap-rollers, the iveight of cotton required would have been 28 
pounds 9J ounces. 

The speed of the calender-rollers, or delivering-balls, is re- 
quired from the following particulars : — 
Revolutions of doffer- cylinder a minute 4.213. 
Wheel on doffer-cylinder end 130 teeth, working carrying- 
wheels, which works into a wheel of 28 teeth on delivering-ball- 
shaft. 

4.213 revolutions of doffer-cylinder a min. 
130 teeth wheel on doffer-cylinder. 



126390 

4213 

Teeth of wheel ^ 

on cal. ball- 1 28)547.690(19.56 revolutions of delivering-balls 
shaft, J 28 a minute. 



267 

252 



156 
140 

169 
168 



Required the speed of the calender-rollers, or delivering-balls, 
from the following particulars : — 

Revolutions of main cylinder a minute, 108.92. 

Wheel on axis of main cylinder, 22 teeth. 

Wheel on stud, 140 teeth. 

Wheel on stud, 32 teeth. 

Wheel on doffer-cylinder end, 130 teeth. — (Working carriers.) 

Wheel on deliver ing-b all-shaft, 28 teeth. 

108.92 revolutions of main cylinder a minute. 
22 teeth wheel on axis of main cylinder. 

21784 
21784 



2396.24 



64 CARDING-ENGINE. 

2396.24 

32 teeth wheel on stud. 



479248 
718872 



76679.68 dividend. 



140 teeth wheel on stud. 
28 teeth wheel on delivering-ball-shaft 



1120 

280 



3920 divisor. 

Divisor. Dividend. 

3920)76679.68(19.56 revols. of delivering-balls a 
3920 minute. 



37479 

35280 

21996 
19600 



23968 
23520 

448 

If the calender-rollers, or delivering-balls, make 19.56 revo- 
lutions a minute, what number of inches, feet, and yards will it 
traverse, if their diameters be 3| inches? 

3.1416 circumference when the diam. is 1. 
3.875 diameter of delivering-balls. 



157080 
219912 
251328 
94248 

12.1737000 



CARDING-ENGINE. 65 

12.1737000 
19.56 revols. of delivering-balls a minute. 



730422 
608685 
1095633 
121737 

1 ft. = 12 in.)238. 117572 inches, delivering-balls traverse a min. 



1 yd. = 3 ft. )19. 843131 feet, delivering-balls traverse a min. 

6.614377 yards, delivering-balls traverse a min. 

Or, 6 yds. 1 ft. 10J in. nearly, the delivering-balls traverse a min. 

The speed of the licker-in is required from the following par- 
ticulars : — 

Revolutions of main cylinder a minute 108.92. 
Diameter of pulley on cylinder, 14 inches. 
Diameter of pulley on licker-in, 7 inches. 

108.92 revols. of main cyl. a minute. 
14 inches diameter of pulley. 



43568 
10892 



Inches diam. of pul. \ h^i ^94 qq 
on licker-in, J ' 

217.84 revolutions of licker-in a min. 

N.B. — The only utility of a licker-in is the innervation of the 
cards on the main cylinder, and whilst many approve of them, 
more disapprove of them. 

The speed of the crank is required from the following par- 
ticulars : — 

Revolutions of main cylinder a minute, 108.92. 
Diameter of pulley on cylinder for driving crank-shaft, 16 inches. 
Diameter of pulley on crank- shaft, 7 inches. 



66 CARDING-ENGINE. 



108.92 revols. of main cyl. a minute. 
16 inches diam. of pulley. 

65352 
10892 



Inches diam. of pul. ) 7)1742 72 
on crank -shaft, ) ' ' 



248.96 or nearly 249 revolutions of 
crank-shaft a minute. 
Required the draught of a carding-engine from the following 
particulars : — 

Lap-rollers at carding-engine traverse 1.862576 inches a minute. 
Calender-rollers, or delivering-balls, traverse 238.117572 inches 
a minute. 

1.862576)238.117572(127.843 draught of carding-engine. 
1862576 



5185997 
3725152 

14608452 
13038032 

15704200 
14900608 



8035920 
7450304 

5856160 

5587728 



268432 

Required the draught of a carding-engine from the following 
particulars : — 

Wheel on calender or delivering-ball-shaft, 28 teeth. 

Wheel on doffer-cylinder end, 130 teeth. 

Wheel on feed-roller-shaft, 13 teeth. 

Wheel on feed-rollers, 128 teeth. 

Wheel on feed-roller end for driving lap-rollers, 17 teeth. 

Wheel on lap-roller end, 46 teeth. 

Diameter of calender or delivering-balls, 3.875 inches. 

Diameter of lap-rollers, 3.75 inches. 



CARDING-ENGINE. 67 

iV. B. — The carrying, or connecting ivheels are omitted, as in 
former examples. 

28 teeth wheel on delivering-ball-shaft. 
13 teeth wheel on feed-roller-shaft. 



84 
28 

364 
17 teeth wheel o 

2548 
364 

6188 
3.75 inches diame 


n feed-roller end, driv 
;er of lap-rollers. 

on doffer-cylinder. 
on feed-rollers. 

on end of lap-roller. 

delivering-balls. 


ing lap- 
rollers 


30940 
43316 
18564 




23205.00 divisor. 

130 teeth wheel 
128 teeth wheel 

3840 

128 




16640 

46 teeth wheel 




99840 
66560 




765440 
3.875 diameter of 




3827200 
5358080 
6123520 
2296320 





2966080.000 dividend. 



68 CAEDING-ENGINE. 

23205)2966080.000(127.8 draught of carding-engine. 
23205 



64558 
46410 

181480 
162435 

190450 
185640 

4810 



If one preparation in the card-room requires 8 carding-engines, 
and each carding-engine delivers 238.117572 inches of carding a 
minute ; what length will the whole preparation of carding-en- 
gines deliver in one day, allowing them to work 10 hours? 

238.117572 in. of carding delivered amin. (1 engine). 
60 minutes 1 hour. 



14287.054320 inches delivered an hour. (1 engine.) 
10 hours equal to 1 day. 



142870.543200 inches delivered a day. (1 engine.) 
8 carding-engines, one preparation. 

inches. 

1 ft.=12)1142964.345600 inches of carding delivered a day from 

1 preparation. 

1 yd. = 3 ft.)95247.0288 feet of carding a day from 1 preparation. 

31749.0096 yds. of carding a day from 1 preparation. 

What length of lap will be required to supply 8 carding-en- 
gines 1 day, allowing them to produce 1142964.3456 inches of 
carding, and the draught at the carding-engine to be 128? 



CARDING-ENGINE. 69 

Inches of carding. 
Draught at card. en. 128)1142964.3456(8929.4 inches of lap re- 

1024 quired. 



1189 
1152 



376 

256 



1204 
1152 



523 
512 

11 

How many weighings of cotton must be fed on the lap machine, 
(each weighing fed on 30 inches of feed-cloth,) to produce 8929.4 
inches of lap, allowing the draught at lap machine to be 2.115; 
and what weight of cotton will it require, allowing each weighing 
to be 24 ounces? 

2.115 draught at lap machine. 
30 inches length of feed. 



63.450 in. of lap each weighing produces. 

63.45)8929.4(140.731, nearly 140f weighings of cotton 
6345 required a day. 



25844 
25380 

46400 
44415 



19850 
19035 



8150 
6345 

1805 



70 CARDING-ENGINE. 



140.731 number of weighings of cotton required a 
24 oz. weight of one weighing. [day. 

562924 
281462 



1 pound is ) 4 )3377.544 
16 oz. j^ 844i386 



211.0965 pounds, or 211 pounds 1J oz. weight of 

16 oz. 1 pound. [cotton required a 

day for 1 prepa- 

5790 ration. 

965 



1.5440 

4 qrs. 



2.1760 



The foregoing examples are considered sufficient, because what- 
ever principle may be considered best, the calculations must be 
made in the same way ; the consumption and production, whether 
single and double carding, or for coarse or fine spinning, maybe 
ascertained with the least trouble and greatest accuracy by a 
strict adherence to the rules and examples illustrated. 

PARTICULARS OF A CARDING-ENGINE. 

Speed of main-cylinder a minute 108.92 revolutions. 

Speed of doffer-cylinder a minute 4.213 revolutions. 

Speed of lap-rollers a minute 0.1581 revolutions. 

Speed of feed-rollers a minute 0.4278 revolutions. 

Speed of licker-in a minute 217.84 revolutions. 

Speed of delivering-balls a minute 19.56 revolutions. 

Speed of crank a minute 248.96 revolutions. 

Diameter of main-cylinder 37 inches, traversing 12657.77 inches 

a minute. 
Diameter of doffer-cylinder 18 inches, traversing 238.24 inches 

a minute. 
Diameter of licker-in 9 inches, traversing 6159.29 inches a 

minute. 



DRAWING-FRAME. 71 

Diameter of lap-rollers 3f inches, traversing 1.862576 inches a 

minute. 
Diameter of feed-rollers 1J inches, traversing 2.016 inches a 

minute. 
Diameter of delivering-balls 3J inches, traversing 238.117572 

inches a minute. 
Diameter of pulley on main-cylinder 14 inches. 
Diameter of pulley on main-cylinder for crank 16 inches. 
Diameter of pulley on crank-shaft 7 inches. 
Diameter of pulley for driving licker-in 14 inches. 
Diameter of pulley on licker-in 7 inches. 
Crank half radius 1J inches, or 3| inches sweep. 
Draught between lap-rollers and feed-rollers 1.08. 
Total draught at carding-engine 128 nearly. 
Weight of lap required to supply a carding-engine 1 day, or 10 

hours 26 pounds 6J ounces. 
Length of carding delivered per engine a day 142870J inches. 
Length of lap consumed by 1 carding-engine a day 1117 \ inches. 

DRAWING-FRAME. 
FIRST HEAD. 

The shaft under the drawing-frame for driving drawing-boxes, 
makes 163.38 revolutions a minute. — Drums on shaft are 12 
inches diameter. — Pulleys on the front rollers are 7 inches di- 
ameter ; the speed of the front roller is required. 

163.38 revols. of shaft a minute. 

12 inches diam. of drums on shaft. 



Inches diam. ofpul. ) />, in/ , A nP 

v . -n r > 6)1960.56 

on front roller, ) ' 

326.76 revolutions of front roller a min. 

If the front roller of a drawing-frame makes 326.76 revolutions 
a minute, and its diameter be \\ inches; what will it traverse? 
326.76 revolutions of front roller a minute. 
1.125 inches diameter of front roller. 



163380 
65352 
32676 
32676 

367.60500 



72 DKAWING-FRAME. 



367.60500 
3.1416 circumference when the diameter is 1. 



2205630 
367605 
1470420 
367605 
1102815 



1154.8678680 nearly 1155 inches, front roller tra- 
verses a minute. 

The speed of shaft under rollers, for driving middle and back 
rollers, is required from the following particulars : — 
Front roller makes 326.76 revolutions a minute. 
Wheel on front roller for driving wheel on shaft 15 teeth. 
Wheel on shaft under-rollers for driving middle and back rollers, 
104 teeth. 

326.76 revolutions of front roller a minute. 
15 teeth wheel on front roller. 



163380 
32676 

Teeth of wheel") 

on shaft under [• 104)4901.40(47.128 revols. of shaft under rols. 
rollers, J 416 

741 

728 

134 
104 

300 

208 

920 

832 

88 



DRAWING-FRAME. 73 

The speed of the middle roller is required from the following 
particulars: — 

Revolutions of shaft under rollers 47.128 a minute. 
Wheel on shaft for driving middle roller 90 teeth. 
Wheel on middle roller 33 teeth. 

47.128 revolutions of shaft under rollers. 
90 teeth wheel on do. [a min. 



Teeth of wheel on ) 33)424L520(12853 revolutions of middle 
micLr01 -> > 33 roller a minute. 



94 

66 

281 
264 

175 
165 

102 

99 

3 

If the middle roller makes 128.58 revolutions a minute, and 
its diameter be 1J- inches ; what will it traverse? 

128.53 revolutions of middle roller a minute, 
1.125 inches diameter of roller. 



64265 

25706 
12853 
12853 

144.59625 

3.1416 circumference when the diameter is L 



86757750 
14459625 
57838500 
14459625 
43378875 454.263579000 inches, middle roller 

*— ~ traverses a minute. 



74 DRAWING-FRAME. 

The draught between the middle and front roller is required, 
from the following particulars: — 

Front roller traverses 1154.867868 inches a minute. 
Middle roller traverses 454.26358 inches a minute. 

454.26358)1154.867868(2.542 draught between middle and 
90852716 front roller. 



246340708 
227131790 

192089180 
181705432 

103837480 
90852716 

12984764 



The speed of the back roller is required, from the following 
particulars : — 

Kevolutions of shaft under rollers, 47.128 a minute. 
Wheel on shaft for delivering back roller, 68 teeth. 
Wheel on back roller, 56 teeth. 

47.128 revols. of shaft under rols. a min. 
68 teeth wheel on shaft. 



377024 

282768 



SaSer! i 56)3204.704(57.22685 revolutions of back roL 

? J zo\) a minute. 

■ 384 

404 336 



392 

12 
112 

15 
112 



— - 480 

127 448 



320 

150 280 



40 



DRAWING-FRAME. 75 

If the back roller makes 57.22585 revolutions a minute, and 
its diameter be 1J inches; what will it traverse? 

57.22685 revols. of back roller a minute. 
1.125 inches diam. of back roller. 



28613425 
11445370 

5722685 
5722685 



64.38020625 

3.1416 circumference when the diam. is 1. 



38628123750 
6438020625 
25752082500 
6438020625 
19314061875 



202.256855955000, or 202J inches, back roller tra- 
verses a minute. 
The draught between the back and middle roller is required, 
from the following particulars : — 

Middle roller traverses 454.26358 inches a minute. 
Back roller traverses 202.25685 inches a minute. 
202.25685)454.26358(2.24597 draught between back and 
40451370 middle roller. 



49749880 
40451370 

92985100 
80902740 

120823600 
101128425 

196951750 
182031165 

149205850 
141579795 

7620055 



76 DRAWING-FRAME. 

N. B. — The total draught of any machine, ivhere there are inter- 
mediate draughts, may be found by multiplying the draughts 
respectively into each other, the sum of ivhich will be the total 
draught. 

The draught may also be found by the wheels, as will appear 
hereafter. 

The speed of the calender-rollers, or delivering-balls, is re- 
quired from the following particulars: — 

Front roller makes 326.76 revolutions a minute. 

Wheel on front roller 38 teeth, working into carrying-wheels. 

Wheel on calender, or delivering-ball-shaft, 100 teeth. 

326.76 revols. of front roller a min. 
38 teeth wheel on front roller. 



261408 

.98028 



d T e^blXft ; On } 10 °) 12416 - 88 



24.1688 revolutions of calender, or 
delivering-balls a minute. 

The draught between the front roller and calender-rollers, or 
delivering-balls, is required from the following particulars: — 
Front roller traverses 1155 inches a minute. 
Calender, or delivering-balls trav. 1170.266 inches a minute. 

1155)1170.266(1.013 draught between front roller 
1155 and delivering-balls. 

1526 
1155 

3716 
3465 

251 



DRAWING-ERAME. 77 

If the calender, or delivering-balls make 24.1688 revolutions 
a minute, and their diameters be 3 inches; what will they tra- 
verse ? 

124.1688 revols. of delivering-balls a minute. 
3 inches diameter of delivering-balls. 



372.5064 

3.1416 circumference when the diam. is 1. 



22350384 
3725064 

14900256 

3725064 
11175192 



1170.26610624 inches, calender-rollers, or deliver- 
ing-balls traverse a minute. 

The draught at the first head of a drawing-frame is required, 
from the following particulars: — 

Back roller makes 57.22685 revolutions a minute. 
Calender, or delivering-balls, make 124.1688 revols. a min« 
Diameter of back roller 1J inch, or 1.125 inch. 
Delivering-balls 3 inches in diameter. 

57.22685 revolutions of back roller a minute. 
1.125 diameter of back roller. 



28613425 
11445370 

5722685 
5722685 



64.38020625 divisor. 

124.1688 revolutions of delivering-balls. 
3 inches diam. of delivering-balls, 

372.5064 dividend. 



78 DRAWING-FRAME. 

64.38)372.5064(5.786 draught at first head of drawing- 
32190 frame. 



50606 
45066 



55404 
51504 

39000 

38628 



372 

The draught at the first head of a drawing-frame is required 
from the following particulars : — 

Calender, or delivering-ball, traverses 1170.2661 inches a minute. 
Back roller traverses 202.2568 inches a minute. 

202.2568)1170.2661(5.786 draught at first head of drawing. 
10112840 



15898210 
14157976 

17402340 
16180544 

12217960 
12135408 

82552 

The draught at the first head of drawing is required from the 
following particulars : — 
Wheel on front roller 15 teeth, working into wheel 104 teeth on 

shaft under rollers. 
Wheel on the other end of shaft under rollers 68 teeth, working 

into wheel on back roller 56 teeth. 
Wheel on calender, or delivering-ball-shaft, 100 teeth, driven by 

carrier-wheels from wheel on front roller, 38 teeth. 
Diameter of back rollers 1J inch, or 1.125 inch. 
Diameter of calender, or delivering-balls 3 inches. 



BRAWING-FRAME. 79 

100 teeth wheel on delivering-ball-shaft. 
15 teeth wheel on front roller. 



1500 

68 teeth wheel on end of shaft on the rols. 



12000 
9000 



102000 
1.125 inch diameter of hack rollers* 



510000 
204000 
1122000 

114750.000 divisor. 



38 teeth wheel on front roller, driving deliv.~ball-sha£t 
104 teeth wheel on shaft nnder roller. 

152 
380 



3952 

56 teeth wheel on back roller. 



23712 

19760 



221312 

3 inches, diameter of delivering-balls. 



14750)663936(5.786 nearly, draught at first head of drawing- 
573750 £ram@. 



901860 

803250 



986100 
918000 

681000 
688500— nearly. 



80 DRAWING-FRAME. 

What length of carding will it require to supply the first head 
of a drawing-frame, having 2 pair of calender, or delivering- 
balls in front, and 6 ends of carding put up at back to each 
pair of calender, or delivering-balls, the back roller traversing 
202.256856 inches a minute ? 

202.256856 or rather more than 202J inches. 
12 ends of carding to 2 pair of balls. 



242T.0822T2 

60 minutes 1 hour. 



145624.936320 inches an hour required. 

If there be 8 carding-engines to a preparation, producing 
1142964 inches a day, how long will it require the first head of 
a drawing-frame to work, to consume what the carding-engines 
produce, allowing the first head of drawing-frame to consume 
145625 inches an hour ? 

145625)1142964(7.8486 hours. 

1019375 60 minutes 1 hour. 



1235890 50.9160, or 7 hours 51 min. nearly . 
1165000 



708900 
582500 

1264000 
1165000 

990000 

873750 

116250 

iV. B.—~It will require the first head of a drawing -frame to worfo 

7 hours 51 minutes successively, to consume the production of 

8 carding-engines, according to the two foregoing examples. 

The consumption and production of any piece of machinery 
will be ascertained in the same way ; therefore it will not be re- 
peated. 



DRAWING-FRAME. 81 

What weight of cotton will it require to be fed on the lap ma- 
chine to produce 1142964 inches of carding a day (which is 
required to supply the first head of drawings), allowing 24 ounces 
of cotton to be fed on 30 inches of feed-cloth at the lap machine, 
and the draught at the carding-engine to be 127.8, and the 
draught at lap machine 2.115 ? 

Multiply the draughts together, and that product by the num- 
ber of inches of feed-cloth that your weight of cotton is fed on 
at lap machine, for a divisor, and the number of inches of carding 
required to supply your drawing-frame, by the weight fed on the 
given number of inches of feed-cloth at lap machine, for a divi- 
dend, and the quotient will be the weight in ounces required. 

127.8 draught at carding-engine. 

2.115 draught at lap machine. 



6390 

1278 
1278 
2556 



270.2970 

30 inches length of feed-cloth at lap 

■ machine. 

8108.9100 divisor. 



142964 inches of carding required. 

24 ounces, weight fed on feed-cloth at lap 

machine. 



4571856 

2285928 



8108.91)27431136(3382.8 ounces, or rather more than 211 
2432673 pounds 8f oz. weight of cotton re- 
quired to be fed on the lap machine. 

3104406 

2432673 



6717330 

6487128 



6802380 

2302020 6487128 

1621782 

315252 



82 DKAWING-FKAME. 

DRAWING-FRAME. 
SECOND HEAD. 

The front rollers of the different heads of a drawing-frame are 
generally of the same speed, and the only difference is the 
draught between the rollers. 

If the front roller makes 326.76 revolutions a minute, the 
revolution of the middle roller is required, from the following 
particulars : — 
Wheel on end of front roller, for driving-shaft under rollers, 14 

teeth. 
Wheel on end of shaft under rollers, 104 teeth. 
Wheel on end of shaft under rollers, driving middle roller, 90 

teeth. 
Wheel on middle roller, 33 teeth. 

104 teeth wheel on shaft under rollers. 
33 teeth wheel on middle roller. 



312 
312 



3432 divisor. 



326.76 revolutions of front roller a minute. 
14 teeth wheel on front roller. 



130704 
32676 



4574.64 

90 teeth wheel on shaft under rollers. 



3432)411717.60(119.9643, or nearly 120 revolutions, 
3432 which middle roller makes 



a mm, 



6851 22080 
3432 20592 



34197 14880 
30888 13728 



33096 11520 
30888 10296 

22080 1224 



DRAWING-FRAME. 83 

If the middle roller at second head of drawing makes 
119.9643 revolutions a minute, what will it traverse, if the di- 
ameter be 1 J inch ? 

119.9643 revolutions of middle roller a min. 
1.125=14- inch diameter of roller. 



5998215 
2399286 
13196073 



134.9598375 

3.1416 circumference when diameter is 1, 



8097590250 
1349598375 
5398393500 
1349598375 
4048795125 



423.98982549000, or nearly 424 inches, the middle 
roller traverses a minute. 

If the front roller of the second head of drawing traverses 
1154.867868 inches, and the middle roller traverses 423.989825 
inches per minute, what draught is there between the middle and 
front rollers ? 

423.989825)1154.867868(2.72 draught between middle and front 
847979650 rols. 



3068882180 
2967928775 

1009534050 
847979650 

161554400 



Required the draught between the middle and front rollers of 
the second head of drawing, from the following particulars : — 
Front roller makes 326.76 revolutions a minute. 
Middle roller makes 119.96 revolutions a minute. 



84 DRAWING-FRAME. 

119.96)326.76(2.72 draught between the middle and front 
23992 rollers, second head of drawing. 

86840 
83972 



28680 
23992 

4688 



The speed of back roller at second head of drawing is required, 
from the following particulars : — 
Speed of front roller, 326.76 revolutions a minute. 
Wheel on end of front roller for driving-shaft under rollers, 14 

teeth. 
Wheel on end of shaft under rollers, 104 teeth. 
Wheel on end of shaft under rollers, driving back roller, 68 teeth. 
Wheel on end of back roller, 56 teeth. 

104 teeth wheel of shaft under roller. 
56 teeth wheel of back roller. 



624 

520 

5824 divisor. 

326.76 revolutions of front roller a minute. 
14 teeth wheel on end of front roller. 


130704 

32676 




4574.64 

68 teeth wheel on 


shaft under rollers 


3659712 

2744784 





311075.52 dividend. 



DRAWING-FRAME. 85 

5824)311075.52(53.412 revolutions of back roller a min. 
29120 



19875 
17472 

24035 
23296 



7392 

5824 

15680 
11648 

4032 

If the back roller at the second head of drawing makes 53.412 
revolutions a minute, and its diameter be 1J inch, what will it 
traverse ? 

53.412 revolutions of back roller a minute. 
1.125 = 14- inch diameter of do. 



267060 

106824 
687532 



60.088500 
3.1416 circumference when the diameter is 1, 



3605310 

600885 
2403540 

600885 
1802655 

188.77403160 inches, the back roller traverses a min* 

The draught between the back and middle rollers, at the second 
head of drawing, is required from the following particulars t— 
Middle roller traverses 424 inches a minute. 
Back roller traverses 188.774 inches a minute. 



86 DRAWING-FRAME. 



188.774)424.000(2.246 draught between middle 
377548 and back rols. 2d head 

of drawing. 



464520 

377548 

869720 
755096 

1146240 
1132644 

13596 

The draught between the back and front roller is required, 
from the following particulars :— 

Front roller traverses 1154.867868 inches a minute. 
Back roller traverses 188.774 inches a minute. 

188.774)1154.867868(6.117 draught between the 
1132644 back and front rols., 

2d head of drawing. 



222238 
188774 



334646 

188774 

1458728 
1321418 

137310 

The total draught at the second head of drawing is required, 
from the following particulars: — 

Wheel on calender or delivering-balls'-shaft, 100 teeth. 

Wheel on front roller, 38 teeth. 

Wheel on front roller, working shaft under front rollers, 14 

teeth. 
Wheel on shaft under rollers, 104 teeth. 
Wheel on shaft under rollers, 68 teeth, working into a wheel 

on back rollers, 56 teeth. 
Diameter of calender or delivering-balls, 3 inches. 
Diameter of back roller, 1J- inch, or 1.125 inch. 



DRAWING-FRAME. 87 

Multiply the number of teeth in the driving-wheels together, 
respectively, and that product by the diameter of the back roller, 
for a divisor, and the number of teeth in the driven-wheels to- 
gether, and that product by the diameter of the calender, or 
delivering-balls, for a dividend, and the quotient will be the real 
or total draught, as in the following example: — 

100 teeth wheel on delivering-ball-shaft. 
14 tth. wheel on front rol., driving-shaft under 

rollers. 

1400 

68 teeth wheel on shaft under rollers. 



11200 

8400 



95200 

9 or 1J inch diameter of back roller. 



856800 divisor. 



38 teeth wheel on front roller. 
104 teeth wheel on shaft under rollers. 



152 

380 



3952 
56 teeth wheel on back roller. 



23712 

19760 



221312 

24 or % 4 = 3 inches, diam. of deliv.-balls. 



885248 
442624 

5311488 



88 DRAWING-FRAME. 

856800)5311488(6.199, or 6.2 nearly, draught between 
5140800 back roller and delivering-balls. 



1706880 
856800 

8500800 
7711200 



7896000 
7711200 

184800 

If the third, or last head of drawing be same as the second 
head, what will the total draught at the three heads of drawing 
be, and what doubling will there be, allowing 6 ends to be put 
up against each pair of calender, or delivering-balls, at each head 
of drawing? 

5.786 draught at first head of drawing. 
6.199 draught at second head of drawing. 

52074 
52074 
5786 
34716 



85.867414 

6.199 draught at third head of drawing. 



322806726 
322806726 
35867414 

215204484 



222.342099386 rather more than 222 T \, total 
draught at the three heads of 
drawing* 



DRAWING-FRAME. 89 



DOUBLING. 

6 ends of carding, first head of drawing-frame. 
6 ends of drawing, second head of drawing-frame. 



36 

6 ends of drawing, third head of drawing-frame. 



216 total doubling at drawing-frame. 

JSf. B. — The above doubling is small, considering the quantity of 
doubling at many places ; however, that may be arranged ac- 
cording to the opinion of managers, $e. 

If two pairs of calender, or delivering-balls, at the first head 
of drawing, traverse 1120.266 inches each pair a minute; what 
length of drawing will they produce in 7.8476 hours, or 7 hours 
51 minutes? 

1120.266 in., delivering-balls traverse a min. 
2 pairs at each head of drawing. 

2240.532 

7.8476 hours. 



13443192 

15683724 
8962128 
17924256 

15683724 

17582.7989232 

60 minutes 1 hour. 



1 ft.^12 in.)1054967.9353920 inches produced in 7.8476 hours. 



1 yard=3 ft.)87913. 994616 feet produced in 7.8476 hours. 

29304.664872 yards produced in 7.8476 hours. 

If the back roller at the second head of drawing traverses 
188.774 inches a minute, and 12 ends be put up; i. e. y 6 ends to 
each pair of delivering-balls; what time must it work to consume 
1054968 inches, which the first head of drawing produces ? 

7 



90 DRAWING-FRAME. 



188.774 inches, back roller traverses a minute. 
12 ends, *. e., 6 to each pair of deliv.-balls. 



2265.288 inches consumed a minute. 

2265.288)1054968.0(465.71 minutes, or 7 hours 45 minutes 

9061152 42f seconds, the second head 

■ ■ must work, to consume what 

14885280 the first head produces. 
13591728 



12935520 
11326440 

16090800 
15857016 

2337840 
2265288 



72552 

If 2 pairs of delivering-balls in front of the first head of draw- 
ing, traverse 1170.266 inches each a minute; what length will 
they produce if they work successively 7 hours 51 minutes, or 
7.8476 hours? 

1170.266 inches, delivering-balls traverse a min. 

2 pairs of deliv.-balls traverse in first head. 



2340.532 

60 minutes 1 hour. 



140431.920 

7.8476 hours. 



84259152 
98302344 
56172768 
112345536 
98302344 



1102053.535392 inches, 2 pairs of delivering-balls at first 
head of drawing produces in 7.8476 hours, or 7 hours 51 min. 



DRAWING-FRAME. 91 

If 12 ends be put up at the second head of drawing, that is. 
6 ends to each pair of delivering-balls, and the back roller tra- 
verses 188.774 inches a minute; what time must the second head 
of drawing work, to consume what the first head produces, say 
1102053.5 inches? 

188.774 inches back roller traverses a minute, 
12 ends. 



2265.288 divisor. 

2265.288)1102053.5(486.5 minutes nearly, or 8 hours 
9061152 6J minutes. 



19593830 
18122304 

14715260 
13591728 



11235320 
11326440— nearly. 

It requires 8 hours 6| minutes for the second head of drawing 
to work, to consume what the first head produces. 

2V. B. — The consumption and production of the third head of 
drawing will be the same as the second head. 



PARTICULARS OP A DRAWING-FRAME. 

First head, front roller, 326.76 revolutions a minute. 
Middle roller, 128.53 revolutions a minute. 
Back roller, 57.226 revolutions a minute. 
Delivering-balls, 124.168 revolutions a minute. 
Diameter of rollers, 1J- inch. 
Diameter of delivering-balls, 3 inches. 
Draught between back and middle rollers, 2.246. 
Draught between middle and front rollers, 2.542. 
Draught between front roller and delivering-balls, 

1.013. 
Total draught at the first head of drawing, 5.786. 



92 TUBE-FRAME. 

Second head, front roller, 326.76 revolutions a minute. 
Middle roller, 120 revolutions a minute. 
Back roller, 53.412 revolutions a minute. 
Delivering-balls, 124.168 revolutions a minute* 
Diameter of rollers, 1J- inch. 
Diameter of delivering-balls, 3 inches. 
Draught between back and middle roller, 2.246. 
Draught between middle and front roller, 2721. 
Total draught at the second head of drawing, 6.123. 

N. B.— The third head of drawing is the same as the second head. 

First head, back roller traverses 202.256 inches a minute. 

Delivering-balls traverse 1170.266 inches a minute. 
Back roller consumes 1142964 inches, or 211ft>s. 8f 

oz. in 7 hours 51 minutes. 
Delivering-balls produce 1102053 inches, or 211ft>s, 
8f oz, in 7 hours 51 minutes. 

Second and third head back rollers traverse 188.774 inches a 

minute. 
Delivering-balls traverse 1170.266 inches a minuteo 
Back rollers consume 1102053 inches, or 211ibs. 8f 

oz. in 8 hours 6J minutes. 
Delivering-balls produce 1102603 inches, or 211ft>s. 

8 j- oz. in 8 hours 6J- minutes. 

ffl. B. — The above weights of drawing are the gross weight of 
cotton; the net weight will be according to its proportionate 
size, or girt, in any operation, as will be shown hereafter. 



TUBE-FRAME. 
The tube-frame is well calculated for coarse and medium yarns, 

SPEEDS, DRAUGHTS, ETC., OF THE TUBE-FRAME. 

Speed of shaft for driving-frame, 143 revolutions a minute. 
Diameter of drum on said shaft, 30 inches. 
Diameter of pulley on frame, 9|, or 9.75 inches. 



TUBE-FRAME. 93 

143 revolutions of shaft a minute. 
30 inches, diameter of drum on shaft. 



Diam. of pulley 9.75 in. )4290. 00(440 revolutions a minute of 
3900 front rollers, second head. 



3900 
3900 



J^.B. — There are 2 sets or tiers of rollers to some of these 
frames; the bach or receiving-rollers are called the first head, 
and the front or delivering -rollers the second head. 

The speed of the middle rollers is required from the following 
particulars : — 

Revolutions of front rollers a minute, 400. 

Wheel on front rollers 21 teeth, working into stud-wheel 42 

teeth. 
Wheel on same stud 30 teeth, working into wheel 32 teeth 

on the end of middle rollers. 

440 revolutions of front roller a minute. 
21 teeth wheel on front roller. 



440 

880 



9240 

30 teeth wheel on stud, 



277200 dividend, 

42 teeth wheel on stud. 

32 teeth wheel on middle roller. 



84 

126 



1344 divisor. 



94 TUBE-FRAME. 

1344)277200(206.25, or 206^ revols. of mid. rols. a min. 

2688 



8400 
8064 

3360 
2688 



6720 
6720 



The speed of the back rollers is required from the following- 
particulars : — 

Kevolutions of front rollers a minute, 440. 
Wheel on front rollers 23 teeth, working into wheel 44 teeth on 
stud; on same stud there is a wheel 20 teeth, working into 
wheel 41 teeth on back rollers. 

44 teeth wheel on stud. 

41 teeth wheel on back roller. 



44 

176 



1804 divisor. 

440 revolutions of front roller a minute. 
23 teeth wheel on front roller. 



1320 

880 



10120 

20 teeth wheel on stud. 



202400 dividend, 



TUBE-FRAME. 95 

1804)202400(112.195 revolutions of back roller a minute. 

1804 



2200 
1804 

3960 
3608 



3520 

1804 

17160 

16236 

9240 

9020 

220 

The speed of the front rollers at the first head is required from 
the following particulars : — 

Revolutions of back roller, second head, a minute, 112.195. 
Wheel on back roller, second head 41 teeth, working into car- 
rying-wheel 41 teeth on stud, which works into wheel 46 teeth 
on front roller, first head. 

112.195 revols. of back roL, 2d head, amino 
41 teeth wheel on back roL, 2d head. 



112195 

448780 

Teeth of wheel ) 

on front rols. V 46)4599.995(99.9, or 100 revols. nearly, front 
first head, ) 414 rols. first head, a min. 

459 
414 

459 
414 

45 



96 TUBE-FRAME. 

The speed of the middle rollers at the first head is required 
from the following particulars : — 
Revolutions of front rollers a minute, 100. 

Wheel on front rollers 21 teeth, working into a wheel on stud 42 
teeth ; wheel 30 teeth on same stud, works into wheel 32 teeth 
on middle roller. 

42 teeth wheel on stud. 

32 teeth wheel on middle roller. 



84 
126 

1344 divisor. 



100 revolutions of front roller a minute. 
21 teeth wheel on it. 



2100 

30 teeth wheel on stud. 



1344)63000(46.875 revols. of mid. rol. a minute. 
5376 



9240 

8064 

11760 
10752 

10080 
9408 

6720 
6720 

The speed of the back roller at the first head is required from 
the following particulars : — ■ 
Revolutions of front rollers a minute, 100. 
Wheel on front rollers 27 teeth, working into stud wheel 58 teeth ; 

on same stud there is a wheel 17 teeth, working into wheel 58 

teeth on back rollers. 



TUBE-FRAME. 97 

58 teeth wheel on stud. 

58 teeth wheel on back rollers. 



464 

290 

3364 divisor. 



100 revolutions of front rollers a minute. 
27 teeth wheel on front rollers. 



2700 

17 teeth in wheel on stud. 



18900 
2700 



3364)45900(13.644 revolutions of back roller a minute. 
3364 



12260 
10092 

21680 

20184 



14960 
13456 

15040 
13456 

1584 

JV. B. — When ivorking the speeds of rollers, the driven-wheels 
multiplied into each other will be the divisor. 

The speed of the friction rollers is required from the following 

particulars : — 

Eevolutions of front rollers, second head, a minute, 440. 

Wheel on front rollers 28 teeth, working into wheel 59 teeth on 
bevil-shaft ; on the other end of bevil-shaft there is a wheel 
32 teeth, working into wheel 50 teeth on friction-roller-shaft. 



98 TUBE-FKAME. 



59 teeth wheel on bevil-shaft. 
50 teeth wheel on friction-roller-shaft. 



2950 divisor. 



440 revolutions of front rollers a minute. 
28 teeth wheel on front rollers. 



3520 

880 



12320 

32 teeth wheel on bevil-shaft. 



24640 
36960 



2950)394240(133.64 revolutions of friction-rols. a minute. 
2950 



9924 
8850 

10740 

8850 

18900 
17700 

12000 

11800 

200 
The speed of the tubes is required from the following par- 
ticulars: — 

Revolutions of pulley-shaft a minute, 440. 
Diameter of pulley on said shaft, 18 inches. 
Diameter of tubes, | inch, or .875 inch. 

440 revolutions of pulley-shaft a min. 
18 inches, diam. of pul. on said shaft. 

3520 

440 

■ 7920 



TUBE-FRAME. 99 

Inches diam. of tubes. 875)7920(9051. 428 revols. of tubes a min. 

7875 



4500 
4375 



1250 

875 

3750 
3500 

2500 
1750 

7500 
7000 

500 

The draught between the back and middle rollers at the first 
head is required from the following particulars : — 

Revolutions of back rollers a minute, 13.644. 
Revolutions of middle rollers a minute, 48.875. 
Diameters of back and middle rollers, 1 inch. 

13.644)46.875(3.435 draught between back and 
40932 middle rollers. 



59430 
54576 

48540 
40932 



76080 
68220 

7860 

The draught between the middle and front rollers is required 
from the following particulars: — 

Revolutions of middle rollers a minute, 46.875. 
Revolutions of front rollers a minute, 100. 



100 TUBE-FRAME. 



Diameter of middle rollers, 1 inch. 



Diameter of front rollers, 1| inch, or 1.125 inch. 
100 revolutions of front rollers a minute. 
1.125 inch diameter of do. 



46.875)112.500(2.4 draught between middle and front rols. 
93750 



187500 
187500 



The total draught at the first head is required from the fol- 
lowing particulars : — 

Draught between back and middle rollers, 3.435. 
Draught between middle and front rollers, 2.4. 
3.435 
2.4 



13740 

6870 



8.2440 nearly 8J total draught, first head. 

The draught between the front roller first head, and the back 
roller second head, is required from the following particulars: — 
Revolutions of front rollers first head a minute, 100. 
Revolutions of back rollers second head a minute, 112.195. 
Diameter of front rollers first head, 1J- inch, or 1.125 inch. 
Diameter of back rollers second head, 1 inch. 

100 revols. of front roller a min. first head. 
1.125 inches diameter of front roller. 



112.500 divisor. 



112.5)112.195(0.997 diminution of draught between 
10125 the two heads of rollers. 



10945 
10125 



8200 

7875 

325 



TUBE-FRAME. 101 

JV. B. — On account of the distance between the first and second 
head of rollers, a draught ivould be injurious. 

The draught between the back and middle rollers at the second 
head is required from the following particulars : — 

Revolutions of back rollers a minute, 112.195. 
Revolutions of middle rollers a minute, 206.25. 
Diameters of middle and back rollers, 1 inch. 

112.195)206.250(1.8383 draught between back and 
112195 middle rollers second head. 



940550 

897560 

429900 

336585 



933150 
897560 

355900 
336585 

19315 

The draught between the middle, and front rollers at the second 
head is required from the following particulars : — 

Revolutions of middle rollers a minute, 206.25, 
Revolutions of front rollers a minute, 440. 
Diameter of middle roller, 1 inch. 
Diameter of front roller, 1J- inch, or 1.125 inch. 
1.125 inch, diameter of front rollers. 

440 revolutions of front rollers a minute* 



45000 

4500 



206.25)495000(2.4 draught between mid. and front rols, 
41250 



82500 
82500 



102 TUBE-FRAME. 

The draught between the front rollers and friction-rollers is 
required from the following particulars : — 

Revolutions of front rollers a minute, 440. 
Revolutions of friction-rollers a minute, 133.64. 
Diameter of friction-rollers, 4 inches. 
Diameter of front rollers, 1J- inch, or 1.125 inch. 
440 revolutions of front rollers. 
1.125 inches diameter of front rollers. 



45000 
4500 



495.000 divisor 



133.64 revolutions of friction-rollers. 

4 inches diameter of friction-rollers. 



495)534.56(1.08 nearly, draught between front 
495 rollers and friction-rollers, 



3956 

8960— nearly. 

The total draught at the second head is required from the 
following particulars : (including draught between front rollers 
and friction-rollers.) 

Draught between back and middle rollers, 1.8383. 
Draught between middle and front rollers, 2.4. 
Draught between front and friction-rollers, 1.08. 

1.8383 draught between back and middle rollers. 
2.4 draught between middle and front rols. 



73532 
36766 



4.41192 draught between back and front rollers. 
1.08 draught between front and friction-rols. 



3529536 
4411920 



4.7648736 total draught between back rollers second 
head, and friction-rollers. 



TUBE-FRAME. 103 

The total draught at a tube-frame is required from the fol- 
lowing particulars : — 

Draught at first head, 8.244 
Draught at second head, and friction-rollers, 4.764 



32976 
49464 

57708 
82976 

39.274416 total draught, 

The total draught at a tube-frame is required from the fol- 
lowing particulars :— 

Wheel on friction-roller-shaft 50 teeth, working into 

Wheel on bevil-shaft 32 teeth. 

Wheel on top of shaft 59 teeth, working into 

Wheel on front roller second head 28 teeth. 

Wheel on front roller second head 23 teeth, working into 

Wheel on stud 44 teeth. 

Wheel on same stud 20 teeth, working into 

Wheel on back roller second head 41 teeth, working into a 

Wheel on stud 41 teeth, which works into 

Wheel on front roller first head 46 teeth. 

W'heel on front roller 27 teeth, working into 

Wheel on stud 58 teeth. 

Wheel on same stud 17 teeth, working into 

Wheel on back roller first head 58 teeth. 

Diameter of friction-pulley, 4 inches. 

Diameter of back roller first head, 1 inch. 

50 teeth wheel on friction-roller-shaft. 

59 teeth wheel on top of bevil-shaft. 



2950 

23 teeth wheel on front roller second head, 



8850 
5900 

67850 

20 teeth wheel on second head, 



1357000 



104 TUBE-FRAME. 



1357000 

41 teeth wheel on stud between the heads. 


1357000 
5428000 




55637000 

27 teeth wheel on 


front roller first head. 


389459000 
111274000 




1502199000 

17 teeth wheel or 


i stud first head. 


10515393000 

1502199000 




25537383000 divisor. 




32 teeth wheel on 
28 teeth wheel on 

256 
64 

896 
44 teeth wheel on 

3584 
3584 


bevil-shaft. 

front roller second head. 

stud second head. 


39424 

41 teeth wheel on 

39424 

157696 


back roller. 


1616384 

46 teeth wheel on 


front roller. 


9698301 
-. — _ 74353664 





TUBE-FRAME, 105 

74353664 

58 teeth "wheel on stud. 



594829312 
371768320 



4312512512 

58 teeth wheel on back roller first 
head. 



34500100096 
21562562560 



250125725696 

4 inches diameter of friction-pulley. 



25537383.000)1000502902.784(39.178 total draught between 
76612149 back rols. first head and 



234381412 

229836447 

45449657 

25537383 

199122748 
178761681 



friction-rols. 



203610674 
204299064— nearly. 

N. B. — The small difference between this and the other method 
arises from the decimal parts; however ', the last method is the 
most accurate. 

If the back rollers at the first head make 13.644 revolutions a 
minute, and their diameter be 1 inch ; what will they traverse ? 



106 TUBE-FRAME. 



13.644 

3.1416 circumference when the diara. is 



81864 
13644 
54576 
13644 

40932 

42.8639904 nearly 43 inches, back rollers tra- 
verse at first head a minute. 

If 22 drawings be put up at the back of the tube-frame, what 
length will it consume a minute, if the back rollers traverse 
42.864 inches a minute? 

42.864 inches back rollers traverse a minute. 
22 drawings put up at the back of the frame. 



85728 
85728 



943.008 inches of drawing consumed a minute. 

What time must a tube-frame work to consume 551027 inches 
of drawing, if it consumes 943 inches a minute? 

943)551027(584 minutes, or 9 hours, 44 minutes 
4715 tube-frame must work successive- 
ly, to consume what the last head 

7952 of drawing produces. 

7544 



4087 

3772 



315 

N.B. — There are 1102054 inches of drawing produced at the 
last head of drawings; but on account of the drawing being 
put up double at the back of the frame, only one-half the length 
is reckoned for consumption, i. e. 551027 inches. 



TUBE-FRAME. 107 

If the front roller of a tube-frame makes 440 revolutions a 
minute, and the diameter of the rollers be 1J- inch; what length 
of roving will the frame produce, if it contains 22 tubes, and 
works 9 hours, 44 minutes successively in 1 day? 

1.125 diameter of front rollers = 1J inch. 
3.1416 circumference when the diameter is 1. 



6750 
1125 
4500 
1125 
3375 



35.343000 

440 revolutions of front rollers a minute. 



1413720 
141372 



1555.0920 inches, each tube receives a minute. 
22 drawings put up at back of the frame. 



3110184 
3110184 



34212.024 inches, or 950 yards, 12 inches, or 1 hank 
110 yards, 12 inches, tube-frame produces a minute, L e., if there 
be no draught betwixt the front rollers and the friction-rollers. 

34212 inches of roving produced a minute. 
584 minutes = 9 hours, 44 minutes. 



136848 
273696 
171060 



( 6)19979808 inches of roving produced. 

lyd. = 36 in A 

{ 6)3329968 



554994.66 



108 TUBE-FEAME. 

Yards in a hank, 840)554994.66(660.7 hanks, or 660 hanks, 4 
5040 leas, 114 yards. 



5099 
5040 



5946 

5880 

66 

If 660 hanks of roving weighs 211 Jibs, what hank roving will 
it be? 

211.5)660.7(3.124, or 3J hank roving nearly. 
6345 



2620 
2115 

5050 
4230 



8200 
8460— nearly. 

JV. B. — If the 21iyibs. of cotton had been carried through all the 
different processes of carding, drawing, and roving, without 
any loss, it would have produced a roving equal to 3.124 hanfo 
to the pound, hut as loss is sustained in the different processes, 
that loss can only be accurately ascertained by working the 
weight of cotton consumed regularly through all the processes, 
and ascertaining the net weight of roving which will be accord- 
ing to the following example. 

If the roving be 3.75 hanks to the pound; what will be the 
net weight of 660.7 hanks, and what weight will be lost at the 
different processes, allowing 211JIbs. to have been consumed at 
the carding-engines ? 



TUBE-FRAME. 109 

Hank roving, 3.75)660. 7(176.1861bs. weight of roving produced 
375 from 21ip>s. of cotton. 



2857 
2625 

2320 
2250 



700 
375 

3250 
3000 

2500 
2250 



250 



211.5ft>s. of cotton consumed at 1 prep, a day. 
176.186Ibs. of roving produced at 1 prep, a day. 

35.314K)S. loss sustained in working through the 
different processes, which is nearly 2J ounces to the pound. 

If a tube-frame produces 176.18 6ft>s. of roving a day; what 
weight of roving will it produce in 6 days? 

176.1863bs. of roving produced a day. 
6 days 



1057.116fts., or 1057ft>s. If oz. a week. 
16 oz. = lib. 



696 
116 



1.856 oz. 

4 qrs. = 1 oz. 



3.424 qrs. 



110 TUBE-FRAME. 



PARTICULARS OF A TUBE-FRAME. 

Revolutions of friction-rollers a minute, 133.64. 
Revolutions of front rollers second head a minute, 440. 
Revolutions of middle rollers second head a minute, 206.25. 
Revolutions of back rollers second head a minute, 112.195. 
Revolutions of front rollers first head a minute, 100. 
Revolutions of middle rollers first head a minute, 46.875. 
Revolutions of back rollers first head a minute, 13.644. 
Revolutions of tubes a minute, 9051.428. 
Diameter of friction-rollers, 4 inches. 
Diameter of tubes, j inch. 

Diameter of front rollers first and second head, 1J- inch. 
Diameter of middle and back rollers first and second head, 1 inch. 
Tube traverses a minute, 24881 inches. 
Friction-rollers traverse a minute, 1679 inches. 
Front rollers second head traverse a minute, 1555 inches. 
Middle rollers second head traverse a minute, 648 inches. 
Back rollers second head traverse a minute, 352.5 inches. 
Front rollers first head traverse a minute, 353.4 inches. 
Middle rollers first head traverse a minute, 147.24 inches. 
Back rollers first head traverse a minute, 42.85 inches. 

DRAUGHTS. 

Draught between back and middle rollers first head, 3.435. 
Draught between middle and front rollers first head, 2.4. 
Draught between front rollers first head and back rollers second 

head, 0.997. 
Draught between back and middle rollers second head, 1.8383. 
Draught between middle and front rollers second head, 2.4. 
Draught between front rollers and friction-rollers, 1.08. 
Total draught at the first head, 8.244. 
Total draught at the second head, 4.4119. 
Total draught at tube-frame, 39.178. 

JST.B. — The consumption and production is according to the 
traversing of the rollers, which in all cases will be found by 
multiplying the number of revolutions of the rollers by their 
circumferences. 

The distance of the rollers from each other must be regulated 
according to the staple and quality of cotton. 



SLABBING-FRAME. Ill 



SLABBING-FRAME. 

The speed of the principal, or main-shaft at slabbing-frame, is 
required from the following particulars? 

Revolutions of shaft a minute driving slabbing-frame, 114. 
Diameter of drum on said shaft, 16 inches. 
Diameter of pulley on frame-shaft, 15 inches. 

114 revols. of driving-shaft a minute. 
16 diameter of drum on driving-shaft. 



684 
114 



Diam. of pulley, 15 in.)1824(121.6 revols. of frame-shaft a min. 
15 



32 
30 



24 
15 

90 

90 

The speed of the front rollers is required from the following 
particulars: — 

Revolutions of frame-shaft a minute, 121.6. 
Wheel on said shaft 64 teeth, working into carrying- wheel 138 
teeth on stud, which works into a wheel 60 teeth on front 
rollers. 

121.6 revols. of frame-shaft a min. 
64 teeth wheel on said shaft. 



4864 
7296 



Wheel on front roller, 60 tth.)7782.4 



129.706 revols. of front rols. a min, 

The speed of the middle rollers is required from the following 
particulars: — 



112 SLABBING-FRAME. 

Revolutions of front rollers a minute, 129.7. 
Wheel on front rollers 24 teeth, working into wheel 70 teeth on 
stud ; on the same stud a wheel 25 -teeth works into wheel 56 
teeth on back rollers; wheel on the other end of back rollers 
30 teeth, working into wheel 64 teeth on stud, which works 
into wheel 27 teeth on middle rollers. 

129.7 revolutions of front rollers a minute. 
24 teeth wheel on front rollers. 

5188 
2594 



3112.8 

25 teeth wheel on stud. (Change pinion. 



155640 
62256 



77820.0 

30 teeth wheel on back roller* 



2334600 dividend. 

70 teeth wheel on stud. 

56 teeth wheel on back rollers. 



3920 
27 teeth wheel on middle roller. 



27440 

7840 



105840 divisor. 

105840)2334600(22.0578 revols. of middle rols. a min. 
211680 

828000 

217800 740880 
211680 



871200 



612000 846720 
529200 

24480 



SLABBING-FRAME. 113 

The speed of the back rollers is required from the following 
particulars : — 

Revolutions of front rollers, a minute, 129.7. 
Wheel on front rollers 24 teeth, working into wheel 70 teeth on 

stud; wheel 25 teeth on same stud, works into wheel 56 teeth 

on back rollers. 

129.7 revolutions of front rollers a min, 
24 teeth wheel on front rollers. 



5188 
2594 



3112.8 

25 teeth wheel on stud. 



155640 

62256 



77820.0 dividend. 

70 teeth wheel on stud. 

56 teeth wheel on back rollers. 



3920 divisor. 

3920)77820(19.852 revolutions of back rols. a minute, 
3920 



38620 
35280 

33400 
31360 



20400 
19600 

8000 

7840 

160 



114 SLABBING-FRAME. 

The traversing of the front, middle, and back rollers, are re- 
quired from the three foregoing examples, allowing the front 
rollers to be 1J inch, and the middle and back rollers 1 inch 
diameter. 

129.7 revolutions of front rollers a minute. 

1.125 inches, diameter of front rollers. 



6485 
2594 

1297 

1297 

145.9125 

3.1416 circumference when diameter is 1. 



8754750 
1459125 
5836500 
1459125 

4377375 

458.39871000 inches, front roller traverses a min. 

22.0578 revolutions of middle rollers a minute. 
3.1416 circumference when the diameter is 1. 



1323468 

220578 
882312 
220578 
661734 



69.29678448 inches, middle rollers traverse a min. 

19.852 revolutions of back rollers a min. 
3.1416 circum. when the diameter is 1. 



119112 

19852 
79408 
19852 
59556 

62.3670432 inches, back rollers traverse a min. 



SLABBING-FRAME. 115 

The draught between the back and middle rollers, the draught 
between the middle and front rollers, and the total draught is 
required from the three foregoing examples ? 

62.367)69.29678(1.111, or rather more than l.J draught 
62367 between back and middle rollers. 



69297 
62367 

69308 
62367 



69410 
62367 

7043 

69.2967)458.39870(6.615 draught between middle and front 
4157802 rollers. 



4261850 
4157802 

1040480 
692967 

3475130 
3464835 

10295 



62.367)458.3987(7.35 draught between back and front rols. 
436569 or total draught at slabbing-frame. 

218297 
187101 



311960 
311835 



125 



116 SLABBING-ERAME. 

The draught between the back and middle rollers is required 
from the following particulars : — 
Wheel on back rollers 30 teeth, working into wheel 64 teeth on 

stud, which works into wheel 27 teeth on middle roller. 
Diameter of back and middle rollers, each 1 inch. 
T tli f hi f ^^ teeth wheel on back rollers, 
middle roller, 27 ) q777 



H draught between back and middle 

rollers. 

The draught between the middle and front rollers is required 
from the following particulars: — 

Wheel on front roller 24 teeth, working into wheel 70 teeth on 
stud; wheel 25 teeth on same stud, working into wheel 56 
teeth on back rollers ; on the other end of back rollers, wheel 
30 teeth working into wheel 64 teeth on stud; same stud wheel 
working wheel 27 teeth on middle rollers. 

Diameter of front rollers, 1J-, or 1.125 inch. 
Diameter of back rollers, 1 inch. 

DRIVING-WHEELS. 

24 teeth wheel on front rollers. 

25 teeth wheel on stud working back rols. 



120 

48 



600 

30 teeth wheel on back rollers. 



18000 

8, or 1 inch diameter of middle rollers. 



44000 divisor. 

DRIVEN-WHEELS. 

70 teeth wheel on stud. 

56 teeth wheel on back rollers. 



3920 



SLABBLNG-FRAME. 117 

3920 

27 teeth wheel on middle rollers. 



27440 

7840 



105840 

9, or ■§ inch diameter of middle rollers. 



144000)952560(6.615 draught between middle and front 
864000 rollers. 



885600 
864000 



216000 
144000 

720000 
720000 

The total draught is required from the following particulars:— 
Wheel on front rollers 24 teeth, working into wheel 70 teeth on 
stud ; wheel on same stud 25 teeth, working into wheel 56 
teeth on back rollers. 

Diameter of back rollers, 1 inch. 

Diameter of front rollers, 1J, or 1.125 inch. 

DRIVING- WHEELS. 

24 teeth wheel on front rollers. 

25 teeth wheel on stud. (Change pinion.) 



120 

48 



600 

8, or 1 inch diameter of back rollers. 



4800 divisor. 



118 SLABBING-FRAME. 



DRIVEN-WHEELS. 

70 teeth wheel on stud. 

56 teeth wheel on back rollers. 

39*20 

9, or 1 J inch diameter of front rollers. 



48.00 



12)352.80 
4) 29.4 



7.35 total draught at slabbing-frame. 

What length of drawing will be required to supply a slabbing- 
frame 1 day (allowing it to work at the rate of 9 hours suc- 
cessively), having 40 spindles, and the back rollers traversing 
62.367 inches a minute? 

62.367 inches, back rollers traverse a min. 
40 spindles in frame. 



2494.680 

9 hours = 1 day. 



22452.120 

60 minutes = 1 hour. 



36 in., 1 yard, 



( 6)1347127.200 inches of drawing required a day, 
1 6)224521.2 



37420.2 yards of drawing, or 44 hanks, 3 
leas, 110J yards, required to supply a slabbing-frame 9 hours, 
or 1 day. 

What time must a slabbing-frame with 40 spindles work a day, 
to consume 1102054 inches of drawing, if it consumes 2494.68 
inches a minute? 



SLABBING-FRAME. 119 

2494.68)1102054(441.76 minutes or 7 hours, 21 minutes, 
997872 45 seconds, the slabbing-frame 

must work to consume what the 

1041820 last head of drawings produces. 

997872 



439480 
249468 

1900120 

1746276 

1538440 

1496808 

41632 

If the front rollers of a slabbing-frame traverse 458.4 inches 
a minute, and the diameter of the rollers be 1J- inch, the number 
of spindles 40 ; what length of slabbing will it produce in 7 hours, 
21 minutes, and 45 seconds, or 441.76 minutes? 

458.4 inches, rollers traverse a minute. 
40 spindles in frame. 



18336.0 slabbing-frame produces a minute. 
441.76 minutes, or 7 hours, 21f minutes. 



110016 
128352 
18336 
73344 
73344 

( 6)8100111.36 inches of slabbing produced in 7 

lyd.=36in. < hours 21f minutes. 

(.6)1350018.56 



1 lea = 120 yds.)225003.0933 yards of slabbing produced in 7 

hours, 21| minutes. 

1 hank = 7 leas)1875.02577 leas of slabbing produced in 7 
hours, 21f minutes. 

267.860822 



120 SLABBING-FRAME. 



267.860822 hanks of slabbing produced in 7 
7 leas, 1 hank, [hours, 21f minutes. 



6.025755 leas. 

120 yards, 1 lea. 



3.090666 yds. or 267 hanks, 6 leas, 3 yds. 

If 267 hanks, 6 leas, and 3 yards, or 267.8608 hanks of slab- 
bing weighs 211 Jibs. ; what hank will it be? 

RULE— Divide the number of hanks by the weight, and the 
quotient will be the hanks in one pound. 

lbs. Hanks. 
211.5)267.8608(1.266 hanks of slabbing in one pound. 
2115 



5636 
4230 

14060 
12690 

13708 
12690 

1018 

If the 2111 Jfog, f cotton had been carried through the dif- 
ferent operations without waste, according to the foregoing dou- 
blings and draughts, it would have produced a slabbing equal to 
1.266, or rather more than 1J- hanks to the pound, but on trying 
the slabbing I find it to be equal to 1.5 hanks to the pound : 
what loss is sustained in working ? 

EULE — Divide the number of hanks produced bj the hank- 
slabbing, which, subtracted from the gross weight of cotton, 
say 211Jft)s., will show the loss sustained in working. 



SLABBING-FRAME. 121 

Hanks 
Hank-slabbing, 1.5)267.8608(178.574, or 178fts. 9 oz. of slab- 
15 bing produced from 211JIbs. 

of cotton. 

117 
105 



128 
120 



86 

75 



110 
105 



58 

60 — nearly. 

Bbs. oz. 

211 . . 8 gross weight of cotton fed on lap machine, 

178 . . 9 net weight of slabbing produced. 



32 . . 15 loss sustained in working. (Flies, strips, &c.) 



TURNS AN INCH ON SLABBING. 

The turns an inch on the slabbing, are required from the fol- 
lowing particulars: — 

Revolutions of frame-shaft a minute, 121.6. 
Wheel on said shaft 90 teeth, working into wheel 138 teeth on 

stud, which works into wheel 46 teeth on shaft for driving 

spindles. 
Wheel on shaft driving spindles, 50 teeth. 
Wheel on spindles, 25 teeth. 
Front rollers traverse 458.3987, or nearly 458.4 inches a minute. 

N. B. — The wheel 138 teeth is a carrying-wheel ; there is another 
wheel 138 teeth which is omitted, it being a carrier also. 



122 SLABBING-FRAME. 



121.6 revolutions of frame-shaft a minute. 
90 teeth in wheel on said shaft. 



10944.0 

50 teeth wheel on spindle-shaft. 



547200 dividend. 

46 teeth wheel (driven) on spindle-shaft. 
25 teeth wheel on spindles. 



230 

92 



1150 divisor, 

1150)547200(475.8 revolutions of spindles a minute, 
4600 



8720 
8050 

6700 
5750 



9500 
9200 

300 

Inches. Revolutions of spindles. 

458.3987)475.8260(1.038 turns an inch on slabbing. 

4583987 



17427300 
13751961 

36753390 
36671896 



81494 



ROVING-FRAME. 123 

ROVING-FRAME. 

The speed of the first propelled-shaft of the roving-frame is 
required from the following particulars : — 

Revolutions of shaft driving roving-frame a minute, 143. 
Diameter of drum on said shaft, 16 inches. 
Diameter of pulley on frame-shaft, 15 inches. 

143 revolutions of shaft a minute. 
16 inches diameter of drum on shaft. 









858 
143 


Inches 
pulley, 


diam. 
15, 


of 


f 5)2288 
1 3)457.6 



152.533 revolutions of first propelled-shaft 
at roving-frame a minute. 

The speed of the front rollers is required from the following 
particulars : — 

Revolutions of frame-shaft a minute, 152.533. 
Wheel on same shaft 54 teeth, working into carrying-wheel 138 
teeth, which works into wheel TO teeth on front rollers. 

152.533 revols. of shaft a minute. 
54 teeth wheel on said shaft. 



610133 

762666 



i>ont h rols Wheel ° n 1^)8236.800 



,117. 66857 revols. of front rollers a min. 

If the front rollers of a roving-frame make 117.66857 revolu- 
tions a minute, and their diameter be 1J-, or 1.125 inch; what 
will they traverse a minute ? 

117.6685 revols. of front rollers a minute. 
1.125, or 1 J inch diameter of front roL 



5883425 
2353370 

1176685 
1176685 
-- ■ ■■ 132.3770625 



124 ROVING-FRAME. 



132.3770625 

3.1416 circumference when diameter is 1, 



7942623750 
1323770625 
5295082500 
1323770625 
3971311875 



415.87577955000 inches, front rol. traverses a min. 

The speed of the middle rollers is required from the following 

particulars: — 

Revolutions of front rollers a minute, 117.6685. 

Wheel on front rollers 24 teeth, working into wheel 70 teeth on 
stud ; on same stud wheel 24 teeth, works into wheel 60 teeth 
on back rollers; wheel 30 teeth on the other end of back 
rollers, works into wheel 64 teeth on stud, which works into 
wheel 24 teeth on middle rollers. 

117.6685 revols. of front rols. a min. 
24 teeth wheel on do. 



4706740 
2353370 



2824.0440 

24 teeth wheel on stud. 



11296176 

5648088 



67777.056 

30 teeth wheel on back rollers. 



2033311.680 dividend. 

70 teeth wheel on stud. 
60 teeth wheel on back rollers. 



4200 

24 teeth wheel on middle rollers. 



16800 
8400 
100800 divisor. 



ROVING-FRAME. 125 

1008.00)20333.11.68(20.1717 revols. of mid. rols. a minute. 
2016 



1731 

1008 



7231 

7056 

1756 

1008 



7488 
7056 



432 

If the middle rollers be 1 inch diameter, making 20.1717 re- 
volutions a minute ; what will they traverse ? 

20.1717 revolutions of middle rollers a minute. 
3.1416 circumference when diameter is 1. 



1210302 
201717 
806868 
201717 
605151 



63.37141272 inches, middle rollers trav. a minute. 

The speed of the back rollers is required from the following 
particulars : — 

Revolutions of front rollers a minute, 117.6685. 
Wheel on front rollers 24 teeth, working into wheel 70 teeth on 
stud; on same stud wheel 24 teeth, works into wheel 60 teeth 
on back rollers. 

117.6685 revolutions of front rollers a minute. 
24 teeth wheel on do. 



4706740 
2353370 

2824.0440 



126 ROVING-FRAME. 

2824.0440 

24 teeth wheel on stud. 



11296176 

5648088 



67777.056 dividend. 



70 teeth wheel on stud. 
60 teeth wheel on back rollers. 



4200 divisor. 



42.00)677.77.056(16.137 revolutions of back rollers 
42 a minute. 



257 

252 



57 

42 

157 
126 

310 

294 

16 

If the back rollers be 1 inch diameter, making 16.137 revolu- 
tions a minute ; what will they traverse ? 

16.137 revolutions of back rollers a minute. 
3.1416 circumference when diameter is 1. 



96822 
16137 
64548 
16137 
48411 

50.6959992, or 50^ inches nearly, back rollers 

traverse a minute. 



ROVING-FRAME. 127 

The draught of roving-frame is required from the following 
particulars : — 

Wheel on front rollers, 24 teeth (driving). 
Wheel on stud, 70 teeth (driven). 
Wheel on same stud, 24 teeth (driving). 
Wheel on back rollers, 60 teeth (driven). 
Diameter of back rollers, 1 inch (driving). 
Diameter of front rollers, 1 J inch (driven). 

DRIVING-WHEELS. 

24 teeth wheel on front rollers. 

24 teeth wheel on stud. (Change pinion.) 



48 



576 

8=1 inch, diameter of back rollers. 



4608 divisor. 



DRIVEN-WHEELS. 



70 teeth wheel on stud, 
60 teeth wheel on back rollers. 



4200 

9, or 1 J- inch, diameter of back rollers,, 



37800 dividend 



4608)37800(8.203 
36864 



9360 
9216 

14400 
13824 

576 

If the back rollers of a roving-frame traverse 50.696 inches 
a minute, with 72 spindles ; what length of slabbing will it con- 



128 ROVING-FRAME. 

sume, allowing the slabbing to be doubled, or 2 ends to each 
spindle ? 

50.696 inches, back rollers traverse a minute. 
72 spindles in frame. 



101392 

354872 



3650.112 

2 slabbings to each spindkc 



7300.224 inches, of slabbing consumed at roving- 
frame a minute. 

If 1 roving-frame consumes 7300.224 inches of slabbing a 
minute ; what time must 2 roving-frames work, to consume 
8100111.36 inches? 

7300.224 inches, consumed a min. by 1 frame. 
2 frames. 



Divisor, 14600.448 inches, 2 frames consume a minute. 



14600.448)8100111.36(554.78 minutes, or 9 hours, 14f minutes, 
73002240 2 roving-frames must work suc- 

cessively, to consume what the 

79988736 slabbing-frame produces. 

73002240 



69864960 

58401792 

114631680 
102203136 

124285440 
116803584 

7481856 



What length of roving will 2 frames, of 72 spindles each, pro- 
duce in 9 hours, 14f minutes, or 554.78 minutes, if the front 
rollers traverse 415.87 inches a minute? 



ROVING-FRAME. 129 

415.87 inches front rollers traverse a minute. 
72 spindles in 1 frame. 



83174 
291109 



29942.64 inches of roving one frame produced a 
2 frames. [minute. 



59885.28 inches of roving 2 frames prod, a min. 
554.78 minutes, or 9 hours, 14} minutes. 



47908224 
41919696 
23954112 
29942640 
29942640 • 

33223155.6384 inches of roving the 2 frames produce 
in 554.78 minutes, or 9 hours 14f min. 

How many hanks of roving are there in 33223155.6384 
inches? 

( 6)33223155.6384 inches of roving. 
1 yard is 36 in. < 

( 6)5537192.6064 

1 hank is 840 yards,)922865.4344(1098.6493 hanks of roving. 
840 7 leas 1 hank. 



8286 4.5451 leas. 

7560 120 yards 1 lea. 



7265 65.4120 yards. 

6720 

7834 



5454 7560 
5040 



-2744 

4143 2520 

3360 

224 



33223155.6384 inches of roving will be 1098.6493 hanks, or 1098 
hanks, 4 leas, and 65 yards. 



130 ROVING-FRAME. 

If 1098 hanks, 4 leas, and 65 yards, or 1098.6493 hanks of 
roving weigh 211J pounds ; what hank will it be ? 
Pounds. Hanks. 

211.5)1098.6493(5.194 hanks roving. 
10575 



4114 
2115 

19999 
19035 

9643 
8460 

1183 

JV. B. — If the 211 %lbs. of cotton could be carried through all the 
different operations in the card room to the roving ivithout 
waste, it would produce a roving equal to 5.194 hanks in the 
pound {allowing the doublings and draughts to be the same, 
as shown informer examples). 

If, on trying the roving, its weight is equal to 6.15 hanks in 
the pound, what weight of roving will there be in 1098.649 
hanks ? 

Hanks. Hanks yarn. 

6.15)1098.649(178.64 pounds of roving. 
615 16 oz. 1 pound. 



4836 
4305 


384 
64 


5314 

4920 


10.24 


3949 
3690 




2590 
2460 





130 



ROVING-FRAME. 131 

Weight of cotton fed on lap machine, 211Sbs. 8 oz. 
Weight of roving produced, - - - 178Sbs. 10J oz. 

Loss sustained in working, - - - 32Ibs. 13f oz. 

The speed of the spindles of roving-frame is required from 
the following particulars: — 
Revolutions of frame-shaft a minute, 152.533. 
Wheel on frame-shaft 68 teeth, working into carrying-wheel 138 
teeth, which works into a wheel 52 teeth on spindle-shaft ; 
wheel 72 teeth on spindle-shaft, works into wheel 18 teeth on 
spindle. 

152.533 revolutions of frame-shaft a minute. 
68 teeth wheel on frame-shaft. 



1220266 
915200 



10372.266 

72 teeth wheel on spindle-shaft for driv- 

ing spindles. 

20744533 
72605866 



746803.200 dividend. 



52 teeth wheel on spindle-shaft. 
18 teeth wheel on spindle. 

416 
52 



936 divisor. 

936)746803.2(797.86 revolutions of roving-frame 

6552 spindles a minute. 

8112 

9160 7488 

8424 

6240 

7363 5616 

6552 

624 



132 THROSTLE-FRAME. 

The turns an inch of roving are required, from the following 
particulars : — 

Revolutions of spindles a minute, 797.86. 
Front rollers traverse a minute, 316 inches. 

316)797.86(2.525 turns an inch of roving. 
632 



1658 
1580 

786 
632 



1540 

1580— nearly. 

The speeds of any moving power belonging to machinery may 
be found in the same manner as illustrated in the foregoing ex- 
amples. 

The construction of the slabbing and roving-frames differs 
materially; every machine-maker having a method of his own, 
whereby to work the different moving powers, belonging to, and 
connected with, the slabbing and roving-frames; while every 
master, manager, and overlooker generally gives a preference 
to some particular machine-maker. 

Improvements in all kinds of machinery are continually pro- 
gressing, but the system of calculations remains the same ; there- 
fore the system being well grounded, and on sure data, the 
improvements possible to be made will be the more easily arrived 
at, and while theory and practice are combined together, it will 
give both pleasure and satisfaction to the mind. 



THROSTLE-FRAME. 

Throstles, like all other machinery, vary in construction 
either in one part or another, and while some persons prefer the 
patent throstles, of which there are several, others give the pre- 
ference to the common throstle; but whatever the construction 
of the machine may be, any person having a thorough knowledge 
of calculations in addition to practice, will be enabled to form a 
proper estimate of machinery according to improvements and 
alterations made. 






THROSTLE-FRAME. 133 

To produce regular yarns, it is very essential to have good 
washers ; in place of round pieces of cloth, many prefer a strip of 
stout washer cloth, of a proper width, and length of the throstle, 
with holes, according to the number and distance of spindles. 
The washers, being stationary, have more power on the bobbins ; 
consequently, the yarns receive the twist more regularly. 

The speed of the tin drum, or cylinder for driving spindles, is 
required from the following particulars: — 
Revolutions of shaft for driving throstles a minute, 153. 
Diameter of drum on said shaft, 24 inches. 
Diameter of pulley on tin drum, or cylinder- shaft for driving 

spindles, 10 inches. 

153 revolutions of shaft a minute. 
24 inches, diam. of drum on shaft. 



612 

306 



Diam. of pulley, 10 in. )3672 



367.2, or 367 \ revolutions of tin drum, 
or cylinder for driving spindles, a minute. 

If the tin drum, or cylinder for driving spindles, makes 367.2 
revolutions a minute ; what number of revolutions will the spin- 
dles make, if the tin drum, or cylinder, be 12 inches diameter, 
and the wharves 1 inch. 

367.2 revols. of tin drum, or cylinder, a min. 
12 inches, diameter of tin drum. 



4406.4 revolutions of spindles a minute. 

The revolutions a minute of the front rollers are required 

from the following particulars: — 

Revolutions of pulley-shaft a minute, 367.2. 

Wheel on same shaft 32 teeth, working into large stud wheel 122 
teeth ; on same stud a wheel 40 teeth, works into carrying- 
wheel 122 teeth, which works into wheel 54 teeth on front 
rollers. 



134 THROSTLE-FRAME. 



367.2 revolutions of pulley-shaft a minute. 
32 teeth wheel on shaft. 



7344 
11016 

11750.4 

40 teeth wheel on stud. 



470016.0 dividend. 

122 teeth wheel on stud. 
54 teeth wheel on end of front rollers. 



488 
610 



6588 divisor. 

6588)470016(71.344 revols. of front rols. a min. 
46116 



8856 
6588 



22680 
19764 

29160 
26352 



28080 
26352 

1728 

If the front rollers of a throstle make 71.344 revolutions a 
minute : what will they traverse if they be 1 inch diameter ? 



THROSTLE-FRAME. 135 

71.344 revolutions of front rollers a inin. 
3.1416 circumference when diameter is 1. 



428064 
71344 
285376 
71344 
214032 

224.1343104 rather more than 224J inches, front 
rollers traverse a minute. 

If the front rollers of a throstle traverse, or deliver 224.134 
inches a minute ; how many hanks a spindle will be produced in 
1 week, if the throstle works successively 60 hours, thus allow- 
ing 9 hours for doffing and other stoppages ? 

224.134 inches, front rollers deliver a min. 
60 minutes, 1 hour. 



13448.040 

60 hours, 1 week. 



( 6)806882.400 inches produced a spindle a week, 

36 inches, 1 yd. < 

(6)134480.4 

1 lea is 12.0 yds. )2241.3.4 yards produced a week. 

1 hank is 7 leas, )186. 77833 leas produced a week. 

26.682619 hanks produced a week. 
7 leas 1 hank. 



4.778333 leas. 

120 yards 1 lea. 



93.340000 yards. 

The length produced a spindle in 60 hours, or 1 week, will be 
26 hanks, 4 leas, and 93 t 4 q yards. 

The speed of the middle rollers is required from the following 
particulars :— 



138 THROSTLE-FRAME. 

Revolutions of front rollers a minute, 71.344. 
Wheel on front rollers 20 teeth, working into stud wheel 90 teeth ; 
on the same stud change wheel 23 teeth, works into wheel 46 
teeth on back rollers; on the other end of back rollers there 
is a wheel 25 teeth, working into carrjing-wheel 36 teeth on 
stud, which works into wheel 19 teeth on middle rollers. 

71.344 revolutions of front rollers a minute. 
20 teeth wheel on front roller. 



1426.880 

23 teeth wheel. (Change pinion/ 



4280640 

2853760 



32818.240 

25 teeth wheel on back rollers. 



16409120 
6563648 



820456.00 dividend. 



90 teeth wheel on stud. 

46 teeth wheel on back rollers. 



4140 

19 teeth wheel on middle rollers. 



37260 
4140 



78660 divisor. 

78660)820456(10.43 revolutions of middle rollers a minute. 
78660 



338560 
314640 

239200 
235980 

3220 



THROSTLE-FRAME. 137 

If the middle rollers of a throstle be f inch diameter, making 
10.43 revolutions a minute ; what will they traverse ? 

10.43 revolutions of middle rollers a minute, 
.75, or f inch diameter of middle rollers. 



5215 
7301 



7.8225 

3.1416 circumference when diameter is 1. 



469350 

78225 
312900 
78225 
234675 

24.57516600 or rather more than24J inches, middle 
rollers traverse a minute. 

The speed of the back rollers of a throstle is required from 
the following particulars : — 
Revolutions of front rollers a minute, 71.344. 
Wheel on front rollers 20 teeth, working into large stud wheel 
90 teeth ; small stud wheel, or change pinion 23 teeth, work- 
ing into wheel 46 teeth on back rollers. 

71.344 revolutions of front rollers a min. 
20 teeth wheel on front rollers. 



1426.880 

23 teeth wheel change pinion. 



428064 
285376 



32818.24 dividend. 

90 teeth wheel on stud. 

46 teeth wheel on back rollers. 



4140 divisor. 



10 



138 THROSTLE-FRAME, 



4140)32818,24(7.927 revolutions of back rollers a 
28980 minute. 



38382 
37260 

11224 

8280 



29440 

28980 

460 

If the back rollers of a throstle be J inch diameter, making 
7.927 revolutions a minute; what will they traverse? 

7.927 revols. of back rollers a minute. 
875 or | inch diam. of back roller* 



39635 
55489 
63416 



6.936125 

3.1416 circumference when diameter is 1. 



41616750 

6936125 
27744500 
6926125 

20808375 

21.7905303000, or rather more than 21f inches, 
back rollers traverse a minute. 

If the back rollers of a throstle traverse 21.79 inches a minute, 
and the middle rollers 24.575 inches ; what draught will there be ? 
21.79)24.575166(1.128 draught between back and 
2179 middle rollers. 



2785 
2179 



6061 17036 

4358 17432— nearly. 



THROSTLE-FRAME. 139 

If the middle rollers of a throstle traverse 24.575166 inches 
a minute, and the front rollers 224.13431; what draught will 
there be between the middle and front rollers? 

- 24.575)224.13431(9.12 draught between middle 
221175 and front rollers. 



29593 
24575 

50181 
49150 

1031 

If the back rollers of a throstle traverse 21.79 inches a minute, 
and the front rollers 224.1343; what draught will there be be- 
tween the front and back rollers? 

21.79)224.1343(10.286 draught between the back 
2179 and front rollers. 



6234 

4358 



18763 

17432 

13310 
13074 



236 

If the driving-wheels be 20 and 23, and the driven-wheels 90 
and 46, the diameter of the front rollers 1 inch, and the back 
rollers £ inch ; what draught will there be ? 

DRIVING-WHEELS. 

20 
23 

460 
Back roller J inch, or 7 



3220 divisor. 



140 THROSTLE-FRAME. 

DRIVEN-WHEELS. 
90 
46 



4140 

8 = 1 inch front rollers. 



3220)33120(10.286 nearly, draught in rols. 
3220 



9200 
6440 



27600 

25760 



18400 
19320— nearly. 

If one spindle produces 26 hanks, 4 leas, and 93 T 4 n yards, or 
26.682622 hanks of twist a week; what length and weight of 
No. 30's twist will 6876 spindles produce? 

26.682622 hanks a spindle a week. 
6876 spindles. 



160095733 
186778355 
213460977 
160095733 



No, of twist, 3.0's)18346.9.709988 hanks of twist a week. 



6115.6569996ifos. of twist a week. 
16 ounces 1 lb. 



39419976 

6569996 



10.5119936 ounces. 

4 qrs. 1 oz. 



2.0479744 

Length of twist produced, 18346.97, nearly 18347 hanks. 
Weight of twist produced, 6115fbs. 10J oz. of No. 30's twist. 



THROSTLE-FRAME. 141 

The speed of the mangle-wheel is required, from the following 
particulars: — 

Revolutions of pulley-shaft a minute, 367.2. 
Wheel on said shaft 32 teeth, working into stud-wheel 122 teeth; 
wheel on same stud 6 teeth, working into Avheel 110 teeth 
on mangle-wheel-shaft ; wheel 8 teeth on mangle-wheel-shaft, 
working into mangle-wheel 82 teeth. 

122 teeth wheel on stud. 
110 teeth wheel on mangle- wheel-shaft. 



13420 

82 teeth mangle-wheel. 



26840 
107360 



1100440 divisor. 

367.2 revolutions of pulley-shaft a minute* 
32 teeth wheel on pulley- shaft 



7344 
11016 

11750.4 

6 teeth wheel on stud. 



70502.4 

8 teeth wheel on mangle-wheel-shaft,, 



1I00440)564019.2(.512539, or rather more than half a 
5502200 revolution of mangle-wheel 



■ a minute. 

1379920 
1100440 

2794800 
2200880 

5939200 

5502200 

10686800 

4370000 9903960 
3301320 



782840 



142 THROSTLE-FRAME. 

The speed of the traverse-shaft is required, from the following 
particulars: — 

Revolution of mangle-wheel a minute, .512539. 
Wheel on mangle-wheel 21 teeth working racks, which works 
into wheel 43 teeth on traverse-shaft. 

.51254 revolution of mangle-wheel a minute. 
21 teeth on mangle-wheel, working racks. 



51254 

102508 

Teeth of wl. ^ 

on traverse- > 43)10. 76334(. 25, or rather more than J of a revo- 
shaft, J 86 lution of traverse-shaft a min. 



216 
215 



What will the traverse move a minute, according to the follow- 
ing particulars : — 

Revolution of traverse-shaft a minute, .25, or J. 
Diameter of pulleys on traverse-shaft, 1J inch. 

3.1416 circumference when diameter is 1. 
1.5, or 1J inch diameter of pulleys on 

• traverse-shaft. 

157080 
31416 



4.71240 

.25 or J- revolution of traverse-shaft. 



235620 
94248 



1.178100, or rather more than 1^ inch, tra- 
verse moves a minute. 

If the front rollers of a throstle traverse, or deliver 224.135 
inches a minute, and the spindles make 4406.4 revolutions a 
minute, how many turns will there be in 1 inch of twist ? 



THROSTLE-FRAME. 143 

Deliv. a min., 224.135 in.)4406.400(19.65958 turns an inch for 

224135 No. 30's twist. 



2165050 
2017215 

1478350 
1344810 

1335400 

1120675 . 

2147250 
2017215 

1300350 
1120675 



1796750 
1793080 



3670 

PARTICULARS OF A THROSTLE-FRAME. 

Revolutions of a tin-drum, or cylinder for driving spindles a 

minute, 367.2. 
Revolutions of spindles a minute, 4406.4. 
Revolutions of front rollers a minute, 71.34426. 
Revolutions of middle rollers a minute, 10.4304. 
Revolutions of back rollers a minute, 7.927. 
Revolution of mangle-wheel a minute, 0.51254. 
Revolution of traverse-shaft a minute, 0.25. 
Diameter of pulleys on drum, or cylinder-shaft, 10 inches. 
Diameter of drum, or cylinder driving spindles, 12 inches. 
Diameter of wharves, 1 inch. 
Diameter of front rollers, 1 inch. 
Diameter of middle rollers, f inch. 
Diameter of pulleys on traverse-shaft, 1J inch. 
Front rollers traverse or deliver a minute, 224.134 inches. 
Middle rollers traverse a minute, 24.57 inches. 
Back rollers traverse or consume a minute, 21.79 inches. 
Traverse or bobbin rail moves a minute, 1.17956 inches. 
Draught between back and middle rollers, 1.2878 nearly. 



144 MULES. 

Draught between middle and front rollers, 9.12. 
Total draught in rollers, 10.286. 
Turns per inch for 30's twist, 19.659, or 19f nearly. 
Hanks per spindle produced, 26 hanks, 4 leas, and 93 t 4 q yards 
a week of sixty hours. 

MULES. 

The speed of the rim-shaft is required from the following par- 
ticulars : — 

Revolutions of shaft for driving upright-shaft in wheel-house, 86. 
Diameter of drum on said shaft, 25 inches. 
Diameter of pulley on upright-shaft in wheel-house, 12 inches. 
Wheel on foot of upright-shaft in wheel-house 68 teeth, working 

into wheel 45 teeth on rim-shaft. 

86 revolutions of shaft a minute. 
25 inches diameter of drum on shaft. 



430 
172 




2150 

68 teeth wheel on foot of upright-shaft 


17200 
12900 




146200 dividend. 




12 inches diameter of pulley on 
45 teeth wheel on rim-shaft. 


upright-shaft in 
[wheel-house. 


540 divisor. 




54.0)14620.0(270.74 revolutions of rim-shaft a 
108 minute. 


382 
378 

990 





400 216 

378 



MULES. 145 

Or thus, -which is preferable when it can be divided by com- 
ponent parts: — 

f 6)14620.0 
54.0^ 



9)2436.66 

270.14 revolutions of rim-shaft a minute. 

The speed of the front rollers is required, from the following 

particulars : — 

Revolutions of rim-shaft a minute, 270.74. 

Wheel on rim-shaft 50 teeth, working into wheel 64 teeth on top 
of long driver-shaft; wheel on bottom of long driver-shaft 40 
teeth, working into wheel 80 teeth on front rollers. 

270.74 revolutions of shaft a minute. 
50 teeth wheel on shaft. 



13537.00 

40 teeth wheel on bottom of long driver. 



541480 dividend. 

64 teeth wheel on top of long driver. 
80 teeth wheel on front rollers. 



5120 divisor. 

512.0)54148.0(105.75 revolutions of front rollers 
512 a minute. 

2948 
2560 

3880 
3584 

2960 
2560 



400 



146 MULES. 

If the front rollers be 1 inch diameter, making 105.75 revolu- 
tions a minute, what will they traverse ? 

105.75 revolutions of front rollers a minute. 
3.1416 circumference when diameter is 1. 



63450 
10575 
42300 
10575 
31725 

332.224200, or 3321J inches, front rollers tra- 
verse a minute. 

The speed of the middle rollers is required, from the following 

particulars : — 

Revolutions of front rollers a minute, 105.75. 

Wheel on front rollers 24 teeth, working into wheel 100 teeth 
on shaft for driving back rollers ; wheel on shaft for driving 
back rollers 25 teeth, working into wheel 50 teeth on back 
rollers ; wheel on back rollers 24 teeth, working into carrying- 
wheel 40 teeth on stud, which works into wheel 21 teeth on 
middle rollers. 

105.75 revolutions of front rollers a minute. 
24 teeth wheel on front roller. 



42300 
21150 



2538.00 

25 teeth wheel (change pinion) on shaft driving 
back rollers. 



12690 
5076 



63450 

24 teeth wheel on back rollers. 



253800 

126900 



1522800 dividend. 



MULES. 147 

100 teeth wheel on shaft driving back rollers. 
50 teeth wheel on back rollers. 



5000 

21 teeth wheel on middle rollers. 



105000 divisor. 

105.000)1522.800(14.5 revolutions of middle rollers a 
105 minute. 



472 
420 



528 
525 



If the middle rollers be | inch diameter, making 14J revolu- 
tions a minute; what will they traverse? 

14.5 revolutions of middle rollers a minute. 
.875, or J- inch diameter of rollers. 



725 
1015 
1160 

12.6875 
3.1416 circumference when diameter is 1. 



761250 

126875 
507500 
126875 
380625 

39.85905000 inches, middle rollers traverse a min. 

The speed of the back rollers is required from the following 
particulars: — 

Eevolutions of middle rollers a minute, 14.5 inches. 
Wheel on middle roller 21 teeth, working into carrying-wheel 40 

teeth on stud, which works into wheel 24 teeth on back rollers. 



148 MULES. 



14.5 revolutions of middle rollers a minute. 
21 teeth wheel on middle roller. 



145 

290 



Teeth of wheel 

24 minute. 



I 24)304.5(12.6875 revolutions of back rollers a 



64 

48 

165 
144 

210 
192 

180 
168 



120 
120 



If the back rollers be f inch diameter, making 12.6875 revo- 
lutions a minute ; what will the y traverse ? 

12.6875 revolutions of back rollers a minute. 
.875, or -J inch diameter of rollers. 



634375 

888125 
1015000 

11.1015625 

3.1416 circumference when diameter is 1. 



666093750 
111015625 
444062500 
111015625 
333046875 



34.87666875000, or 34J inches, back rollers traverse 
a minute. 



MULES. 149 

The draught between the back and middle rollers is required 
from the following particulars: — 

Middle rollers traverse a minute, 39.859. 
Back rollers traverse a minute, 34.876. 

34.876)39.859(1.14288 draught between back and 
34876 middle rollers. 



49830 
34876 

149540 
139504 

100360 
69752 

306080 
279008 

270720 
279008— nearly. 

The draught between the front and middle rollers is required 
from the following particulars : — 

Front rollers traverse a minute, 332.2242 inches. 
Middle rollers traverse a minute, 39.859 inches. 
39.859)332.2242(8.3349 draught between front and mid. rols. 
318872 



133522 
119577 



139450 
119577 

198730 
159436 

392940 
358731 

34209 



150 MULES- 

The draught between the front and back rollers is required 
from the following particulars: — - 

Front rollers traverse a minute, 332.2242 inches. 
Back rollers traverse a minute, 34.8766 inches. 

34.8766)332.2242(9.525 draught between back and 
3138894 front rollers. 



1833480 
1743830 



896500 
697532 

1989680 
1743830 

245850 

The draught in rollers at mules is required from the following 

particulars: — 

Wheel on front rollers 24 teeth, working into wheel 100 teeth on 
shaft for driving back rollers ; change wheel 25 teeth on same 
shaft, works into wheel 50 teeth on back rollers. 

Diameter of back rollers, -J inch. 

Diameter of front rollers, 1 inch. 

DRIVING- WHEELS. 

24 teeth wheel on front roller. 

25 teeth wheel, or change pinion. 



120 

48 

600 
.875, or | inch diameter of back rollers. 



525.000 divisor. 

DRIVEN-WIIEELS. 

100 teeth wheel on shaft for driving back rollers. 
50 teeth wheel on do. 

5000 

1 inch diameter of front rollers. 

5000 dividend. 



MULES. 151 

525)5000(9.524 draught between back and front 
4725 rollers. 



2750 
2625 

1250 
1050 

2000 
2100— nearly. 

JV". B.— The small difference between this and the last example? 
arises from the decimal fractions, ivhich occur in the other sys- 
tem of working. 

If the front rollers deliver 55 inches each stretch, which puts 
up 60 inches; the gain or draught in the carriage will be 5 inches, 
which is equal to ly 1 ^ draught; the draught in the rollers is 
9.524 ; what will the total draught be ? 

9.524 draught in rollers. 

60 inches length of stretch. 



r 5)571.440 

Delivd. from rols. 55 in. < — 

(11)114.288 

10.3899, or 10 T 3 ^ (nearly), total 
draught at mules. 

If the total draught at mules be 10.39, and the numbers to be 
spun 40's ; the length required to be spun 20 hanks a spindle a 
week, the number of spindles in the mules 1000; what hank 
roving will be required, what number of hanks, and what weight? 



RULE. 

Multiply the number of spindles in the mules, by the number 
of hanks required a spindle, and the product will be the total 
number of hanks of yarn produced a week ; which, divided by 
the draught, will give the number of hanks of roving required. 
Then divide the numbers of yarn by the draught in the mules, 
and the quotient will be the hank roving. Then divide the 



152 MULES. 

number of hanks of roving required to produce the given length 
of yarn, by the hank roving, and the quotient will be the weight 
of roving required. 

EXAMPLE. 

1000 number of spindles in mules. 

20 hanks, length required a spindle. 



20000 total number of hanks. 

Hanks. 
Draught 10.39)20000(1925 nearly, hanks of roving required. 
1039 



9610 
9351 



2590 

2078 

5120 

5195 — nearly. 

ISTos. of yarn. 
Draught 10.39)40.00(3.85 hank roving required. 
3117 



8830 
8312 

5180 

5195 — nearly. 

Hanks. 
Hank roving, 3.85)1925(500Ibs. net weight of roving required. 
1925 

The speed of the scroll is required from the following par- 
ticulars : — 

Revolutions of rim-shaft a minute, 270.74. 
Wheel on rim-shaft 20 teeth, working into wheel 60 teeth on 

short driving-shaft. 
Wheel on bottom end of short driving-shaft, 32 teeth, working 

into wheel 100 teeth on scroll-shaft. 



MULES. 153 

270.74 revolutions of rim-shaft a min. 
20 teeth wheel on rim-shaft. 



5414.80 

32 teeth wheel on bottom end of short 
■ ■ driver. 



108296 
162444 



173273.6 dividend. 

60 teeth wheel on top of short driver. 
100 teeth wheel on scroll-shaft. 



6000 divisor. 
6.000)173.273.6 



28.879 nearly, revols. of scroll-shaft a min. 

If the scroll makes 28.879 revolutions a minute, and be 4 
inches diameter ; what will it traverse ? 

28.879 revolutions of scroll a minute. 
4 inches, diameter of scroll. 



115.516 
3.1416 circumference when diameter is 1. 



693096 
115516 
462064 
115516 
346548 

362.9050656 nearly 363 inches, scroll trav. a min. 

The gain, or draught in carriage is required from the follow- 
ing particulars : — 

Scroll traverses a minute, 362.9050656 inches. 
Front rollers traverse a minute, 332.2242 inches. 
11 



154 MULES. 



332.2242)362.9050656(1.09235 gain, or draught in 
3322242 carriage. 



30680865 
29900178 

7806876 
6644484 

11623920 

9966726 

16571940 
16611210— nearly. 

By multiplying the draught in rollers, by the draught, or gain 
in carriage, it will give the total draught at mules. 

If the length of the stretch be 61 inches, and the gain or 
draught in carriage be 1.09235, what length will the rollers 
deliver, and how many inches will the carriage gain a stretch? 

Inches stretch. 
Draught at carriage, 1.09235)61.00000(55.8429 inches, delivered 

546175 at rollers a minute, 



638250 
546175 



920750 
873880 

468700 
436940 

317600 

218470 

991300 
983115 

8185 



MULES. 155 



61.0000 inches, length of stretch. 
55.8429 inches, delivered at rollers. 



5.1571 inches, carriage gains. 

The speed of the spindles at mules is required from the fol- 
lowing particulars : — 

Revolutions of rim-shaft a minute, 270.74. 
Diameter of rim, 23J inches. 
Diameter of rim-band-pulley, 18J- inches. 
Diameter of twist-pulley, 14J inches. 
Diameter of drums in carriage, 10 inches. 
Diameter of wharves, f inch. 

270.74 revolutions of rim a minute. 
23.25 inches, diameter of rim. 



135370 
54148 

81222 
54148 



6294.7050 

14.25 inches, diameter of twist-pulley. 



31473525 

12589410 
25178820 
6294705 



89699.54625 dividend. 

18.25 inches, diameter of rim-band-pulley. 
.75, or f inch, diameter of wharves. 

9125 

12775 



13.6875 divisor. 



156 MULES. 



13.687)89699.54625(65.536 revolutions of spindles 
82122 at mules a minute. 



75775 
68435 

73404 

68435 



49696 
41061 

86352 
82122 

4230 

If the scroll at a pair of mules traverse at the rate of 363 
inches a minute, and the spindles make 6553 revolutions; how 
many turns an inch will there be in the yarn ? 

363)6553(18.05 turns an inch in yarn, while carriage is 
363 coming out. 



2923 

2904 



1900 

1815 

85 

How many turns will the rim make a stretch, if the front 
rollers deliver 57 inches, allowing the rim to make 271 revolu- 
tions, while the front rollers deliver 332.224 inches? 

RULE. — Multiply the revolutions of the rim by the length of 
the stretch, and divide by the number of inches delivered at 
the front rollers, and the quotient will be the revolutions, or 
turns of rim a stretch. 



MULES. 157 

271 revolutions of rim. 
57 inches length of stretch. 



1897 
1355 



Inches delivered, 332.224)15447.000(46.4957 revolutions, -or 

1328896 turns of rim a 
stretch. 



2158040 
1993344 

1646960 

1328896 



3180640 

2990016 

1906240 
1661120 

2451200 

2325568 

125632 

To find the number of turns required for twist, or weft an inch. 

RULE. — For twist, multiply the square root of the numbers, or 
counts of yarn by 3.75, or 3f, and for weft, multiply the 
square root of the numbers, or counts of yarn by 3.25, or 3J, 
and the products will be the turns an inch required. 

What number of turns an inch will 44's twist require, accord- 
ing to the foregoing rule ? 

COUNTS. 

44(6.633 square root of 44. 
36 



126)800 
756 




1323)4400 
3969 


39789 


13263)43100 


3311 



158 MULES. 



6.633 square root of 44, 
3.75, or 3f . 



33165 
46431 

19899 



24.87375, or nearly 25 turns an inch, required for 

No. 44's twist* 

What number of turns an inch will 36's weft require? 
6 is the square root of 36. 
3.25 



19.50, or 19 J turns an inch required for 36's weft* 

What number of turns an inch will 100's twist require? 
10 is the square root of 100, 
3.75 



37.50, or 37 J turns an inch required for No. 100 ? s 

twist . 

The preceding rules for ascertaining the turns an inch required 
for twist and weft, have been generally adopted ; however, where 
a good, or even a fair quality of cotton is used, the following 
rule will be found to answer, particularly for some qualities of 
yarns. 

RULE. — Multiply the numbers, or counts of yarn by 12, the 
square root of which gives the turns an inch required for twist. 
Weft will require 3J, or 4 turns an inch less than twist. 

JV. B. — Some cotton requires more twist than others, according 
to its quality. 

What number of turns an inch will be required for No. 50's 
twist, or weft, according to the above rule? 

50's numbers, or counts of yarn. 
12 



600(25 turns nearly, required for 50's twist, less 
4 3 J turns for weft. 



45)200 

225— nearly. 



MULES. 159 

What number of turns an incli will be required for 100's twist, 
or weft? 

100's numbers, or counts of yarn. 
12 



1200(34.64 turns an inch required for No. 100's 
9 twist, less 3 J turns, which will be equal 

to 31.14 turns an inch for 100's weft 

64)300 
256 



686)4400 
4116 



6924^28400 
27696 



704 

RULE for ascertaining the revolutions of spindles, for the rim 
1. — Multiply the diameters of the driving-pulleys together for 
a dividend, and the driven-pulleys accordingly for a divisor, 
and the quotient will be the revolutions of the spindles for the 
rim 1. 

If the rim and rim-band-pulleys be each 22 inches diameter, 
the twist pulley 13J inches, and the wharves j inch ; what revo- 
lutions or turns will the spindles make for the rim 1 ? 

N. B. — The rim and rim-band-pulley being of the same diameters 
are omitted in the working. 

Diameter of wharves, .875)13.500(15.428 revolutions of spindles 

875 for rim 1. 

4750 
4375 

3750 
3500 

2500 
1750 

7500 — 
7000 500 



160 MULES. 

If the rim be 33 inches diameter, the rim-band-pulley 26 
inches, the twist-pulley 14J inches, and the wharves f of an 
inch ; what number of revolutions, or turns will the spindles 
make for the rim 1? 

DRIVERS. 

Twist-pulley, 14.25 inches. 
Rim, 33 inches. 



4275 
42T5 



470.25 dividend. 

DRIVEN. • 

26 inches drum-band-pulley. 
.75, or J inch wharves. 



130 

182 



19.50 divisor* 

195.)470.25(24.115 revols. of spindles for rim 1 
390 



802 
780 



225 
195 

300 
195 

1050 
975 

75 



BELL-WHEEL, OR REVOLUTIONS OF RIM A STRETCH. 

RULE. — Multiply the turns required an inch, by the number of 
inches in the length of the stretch, for a dividend, and divide 



MULES. 161 

by the revolutions, or turns the spindles make for the rim 1, 
and the quotient will be the number of teeth for the bell- wheel, 
or revolutions of rim a stretch. 

If 18.62 turns an inch be required, and the length of the 
stretch be 58 inches, the revolutions or turns of spindles 15.428 
for the rim 1 ; what number of teeth must there be in the bell- 
wheel, or what revolutions must the rim make a stretch? 

18.62 turns required an inch. 
58 inches, length of stretch. 



14896 
9310 



15.428)1079.96(70 teeth required for bell-wheel, or re- 
107996 volutions of rim a stretch. 

The turns an inch are required from the following particulars : — 
Bell- wheel, 70 teeth; rim, 22 inches diameter; rim-band-pulley, 
22 inches diameter; twist-pulley, 13J inches diameter; drums 
in carriage, 10 inches diameter; wharves, J, or .875 inch 
diameter, and length of stretch, 58 inches. 

N.B. — The rim, rim-band, pulley, and drum in carriage are 
omitted, on account of being drivers and driven of the same 
dimensions. 

Multiply the number of teeth in the bell-wheel, by the diame- 
ters of the driving-pulleys respectively for a dividend; then 
multiply the number of inches in the length of a stretch, by the 
diameters of the driven-pulleys accordingly for a divisor, and the 
quotient will be the revolutions or turns an inch. 
58 inches, length of stretch. 
• .875, or | inch, diameter of wharves. 



7000 
4375 



50.750 divisor. 

13.5 or 13J inches, diameter of twist-pulley. 
70 teeth bell-wheel, or revols. of rim a stretch. 



94.5000 



162 MULES. 

50.75)94.5000(18.62 turns an inch. 

50T5 



43750 
40600 

31500 
30450 



10500 
10150 

350 

If 26 turns an inch be required, and the length of the stretch 
be 61 inches; the revolutions, or turns of the spindles 24.115 for 
the rim 1 ; what number of teeth must there be in the bell-wheel, 
or what revolutions must the rim make a stretch ? 

26 turns an inch. 

61 inches, length of stretch. 



26 
156 



24.115)1586.000(65.768, or nearly 66 teeth required 
144690 for bell-wheel, or revolu- 
tions of rim a stretch. 

139100 

120575 



185250 

168805 

164450 
144690 

197600 
192920 



4680 

The turns an inch are required from the following particulars : — 
Bell-wheel, 66 teeth ; length of stretch, 60 inches ; diameter of 
rim, 33 inches; diameter of rim-band-pulley, 26 inches; diame- 
ter of twist-pulley, 14 J inches; diameter of drums in carriage, 
10 inches, and diameter of wharves, f inch. 



MULES. 163 



66 teeth bell-wheel. 

33 inches, diameter of rim. 



198 
198 



2178 

14.25, or 14J inches, diameter of twist-pulley. 



10890 
4356 

8712 
2178 

31036.50 dividend. 



26 inches, diameter of twist-pulley. 
60 inches, length of stretch. 



1560 
.75, or f inch, diameter of wharves. 



7800 
10920 

1170.00 divisor. 

1170.)31036.5(26.52 turns an inch required. 
2340 



7636 

7020 

6165 

5850 



3150 
2340 

810 



Whatever the principle of the mules is, any particular may be 
found by attending to the rules and examples illustrated. 
JN". B. — The general rules are exemplified ivith the different tables, 

and will appear in their regular course. 



164 TABLES. 

TABLES, 

Showing the size, hank, and proportion of hank in every ope- 
ration, from the lap machine through all the various processes of 
carding, drawing, slabbing, roving and spinning, with practical 
rules and examples. 



EXPLANATION OP THE CARDING AND DRAWING-TABLES. 

The first line in the carding and drawing-table is the decimal 
of the hank according to its length and weight, which will be 
found in the following manner: Multiply all the draughts to- 
gether as far as regards the operation you intend trying, whether 
it be slabbing, drawing, or carding, for a dividend, and all the 
doubling accordingly for a divisor, the quotient will be the 
draught ; then divide the numbers you are spinning, or the num- 
bers you wish to spin, by the net draught, and the quotient will 
be the decimal of the hank ; opposite to which in the table, you 
will have the weight according to the length weighed. 

EXAMPLE. 

Suppose the total draught to be 181440, the doubling 1728, 
and the numbers to be spun 40's ; what weight will 2 yards of 
carding, or doubling be ? 

1728)181440(105 draught more than doubling. 

1728 



8640 
8640 

Counts, 
fraught more than 105)40>0(0j38 decimal of a hank. Opposite 



doubling, ) Q15 



to which in the table under 
- — - 2 yards will be found, 1 dwt. 
850 19.8 grains, the weight re- 
840 quired. 



10 



CARDING AND DRAWING-TABLE. 



1G5 



CARDING AND DRAWING-TABLE. 

From .05 to .089 decimal of hank for 2, 4, and 6 yards. 



Dec. of 
hank. 


2 : 


fards. 


Dec. of 


4 yards. 


Dec. of 
hank. 1 


6 yards. 


dwts. 


grains. 


hank. 


oz. 


dwts. 


grains. 


oz. 


dwts.i 


grains, j 


.05 


13 


21.33 


.05 




9 


13.16 


.05 | 2 


5 


5. 


.051 


13 


14.78 


.051 




9 


0.06 


.051 2 


4 


9.35 


.052 


13 


8.51 


.052 




8 


11.52 


.052 


2 


3 


14.53 


.053 


13 


2.46 


.053 




7 


23.43 


.053 


2 


2 


20.39 1 


.054 


12 


20.64 


.054 




7 


11.78 


.0541 


2 


2 


2.92 


.055 


12 


15.03 


.055 




7 


0.56 


.055 


2 


1 


10.09 


.056 


12 


9.61 


.056 




6 


13.73 


.056 


2 





17.85 


.057 


12 


4.39 


.057 




6 


3.29 


.057! 


2 





2.18 


.058 


11 


23.35 


.058 




5 


17.21 


.058 


1 


17 J 


16.56 


.059 


Jl 


18.48 


.059 




5 


7.47 


.059 


1 


17 


1.95 


.06 


11 


13.77 


.06 




4 


22.05 


.06 


1 


16 


11.83 


.061 


11 


9.22 


.061 




4 


12.94 


.061 


1 


15 


22.17 


.062 


11 


4.81 


.062 




4 


4.13 


.062 


1 


15 


8.95 
20.15 


.063 


11 


0.55 


.063 




3 


19.6 


.063 


1 


14 


.064 


11 


20.41 


.064 




3 


11.33 


.064 


1 


14 


7.74 


.065 


10 


16.41 


.065 




3 


3.32 


.065 


1 


13 


19.73 


.066 


10 


12.52 


.066 




2 


19.55 


.066 


1 


13 


8.07 


.067 


10 


8.75 


.067 




2 


12.01 


.067 


1 


12 


20.76 I 


.068 


10 


5.09 


.068 




2 


4.69 


.068 


1 


12 


9.79 1 


.069 


10 


1.45 


.069 




1 


21.41 


.069 


1 


11 


22.87 


.07 


9 


22.09 


.07 




1 


14.69 


.07 


1 


11 


12.5 S 


.071 


9 


18.74 


.071 




1 


7.98 


.071 


1 


11 


2.72 


.072 


9 


15.89 


.072 




1 


2.29 


.072 


1 


10 


18.19 


.073 


9 


12.31 


.073 







19.12 


.073 


1 


10 


7.43 


.074 


9 


9.22 


.074 1 





12.95 


.074 


1 


9 


22.17 


.075 


9 


6.22 


.075 1 





6.94 


.075 


1 


9 


13.21 


.076 


9 


3.29 


.076 1 





1.1 


.076 


1 


9 


4.39 


.077 


9 


0.45 


.077 


18 


0.9 


.077 


1 


8 


19.85 1 


.078 


8 


21.67 


.078 


17 


19.35 


.078 


1 


8 


11.52 


.079 


8 


18.97 


.079 


17 


13.94 


.079 


1 


8 


3.41 


.08 


8 


16.33 


.08 


17 


8.66 


.08 


1 


7 


19.5 


.081 


8 


13.76 


.081 


17 


3.52 


.081 


1 


7 


11.78 


.082 


8 


11.25 


.082 


16 


22.5 


.082 


1 


7 


4.25 


.083 


8 


8.8 


.083 


16 


17.6 


.083 


1 


6 


20.9 


.084 


8 


6.41 


.084 | 


16 


12.82 


.084 


1 


6 


13.37 


.085 


8 


4.07 


.085 




16 


8.15 


.085 


1 


6 


6.73 


.086 


8 


1.79 


.086 




16 


3.59 


.086 


1 


5 


23.89 


.087 


7 


23.57 


.087 




15 


23.14 


.087 


1 


5 


17.21 


.088 


7 


21.39 


.088 


15 


18.78 


.088 


1 


5 


10.68 


.089 


7 


19.26 


.089 


15 


14.53 


.089 


1 


5 


4.29 



166 EXAMPLES. 

What will 8 yards of .08, or T f ^ hank weigh ? 
Proportion of hank, .08)66.66 

No. of grains in 1 oz., 437.5)833.33 grains,(l oz. 

437.5 



1 dwt. is 24 grains,)395.83(16 dwts. 
24 



155 
144 



11.83 grains. 
Weight of 8 yards of .08 decimal of hank drawing, will be 1 
oz., 16 dwts., 11.83 grains. 

If 8 yards of drawing weigh 1 oz., 16 dwts., 11.83 grains, 
what size or proportion of hank will it be ? 

1 ounce 437.5 grains. 

16 dwts. x 24 grains 384. grains. 

11.833 grains. 



1 oz., 16 dwts., 11.83 grains, 833.333 
The dividend for 8 yards is 66.666. 

833.33)66.6666(.08 decimal of a hank, or size of 
666666 drawing. 

What will 6 yards of .1, or ^ hank drawing weigh ? 

Dividend for 6 yards is 50. (See Table of Dividends.) 
0.1)50, 



500 grains weight. 
1 ounce,437.5 grains, )500. 0(1 oz. 
437.5 



1 dwt. is 24 grains,)62.5(2 dwts. 
48 



14.5 grains. 
Weight of 6 yards of 0.1, or ^ hank drawing, will weigh 1 
oz., 2 dwts., 14 J- grains. 



CARDING AND DRAWING-TABLE. 



167 



CARDING AND DRAWING-TABLE. 
From .09 to .129 decimal of hank for 2, 4, and 6 yards. 



Dec. of 
hank. 


2 yards. 


Dec. of 

hank. 


4 yards. 


Dec. of 
hank. 


6 yards. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


.09 


7 


17.18 


.09 




15 


10.37 


.09 


1 


4 


22.05 


.091 


7 


15.15 


.091 




15 


6.3 


.091 


1 


4 


15.95 


.092 


7 


13.15 


.092 




15 


2.31 


.092 


1 


4 


9.97 


.093 


7 


11.21 


.093 




14 


22.42 


.093 


1 


4 


4.13 


.094 


7 


9.3 


.094 




14 


18.6 


.094 


1 


3 


22.41 


.095 


7 


7.43 


.095 




14 


14.87 


.095 


1 


3 


16.81 


.096 


7 


5.61 


.096 




14 


11.22 


.096 


I 


3 


11.33 


.097 


7 


3.82 


.097 




14 


7.64 


.097 


1 


3 


5.96 


.098 


7 


2.06 


.098 




14 


4.13 


.098 


1 


3 


0.7 


.099 


7 


0.35 


.099 




14 


0.7 


.099 


1 


2 


19.55 


.1 


6 


22.66 


.1 




13 


21.33 


.1 


1 


2 


14.5 


.101 


6 


21.01 


.101 




13 


18.03 


.101 


1 


2 


9.05 


.102 


6 


19.39 


.102 




13 


14.79 


.102 


1 


2 


4.69 


.103 


6 


17.81 


.103 




13 


11.62 


.103 


1 




23.93 


.104 


6 


16.25 


.104 




13 


8.51 


.104 


1 




19.26 


.105 


6 


14.72 


.105 




13 


5.46 


.105 


1 




14.68 


.106 


6 


13.13 


.106 




13 


2.27 


.106 
.107 


1 




9.91 


.107 


6 


11.76 


.1071 


12 


23.52 


1 




5.78 


.108 


6 


10.32 


.108 


12 


20.64 


.108 


1 




1.46 


.109 


6 


8.9 


.1091 


12 


17.81 


.109 


1 





21.21 


.11 


6 


7.51 


.11 


12 


15.03 


.11 


1 





17.04 


.111 


6 


6.15 


.111 


12 


12.3 


.111 


1 





12.95 


.112 


6 


4.98 


.112 




12 


9.97 


.112 


1 





9.46 


.113 


6 


3.49 


.113 




12 


6.98 


.113 


1 





4.97 


.114 


6 


2.19 


.114 




12 


4.39 


.114 


1 





1.09 


.115 


6 


0.92 


.115 




12 


1.85 


.115 




18 


2.78 


.116 


5 


23.67 


.116 




11 


23.35 


.116 




17 


23.03 


.117 


5 


22.45 


.117 




11 


20.9 


.117 




17 


19.35 


.118 


5 


21.24 


.118 




11 


18.48 


.118 




17 


15.72 


.119 


5 


20.05 


.119 




11 


16.11 


.119 




17 


12.16 


.12 


5 


18.88 


.12 




11 


13.77 


.12 




17 


8.66 


.121 


5 


17.74 


.121 


11 


11.48 


.121 




17 


5.22 


.122 


5 


16.61 


.122 




11 


9.22 


.122 




17 


1.83 


.123 


5 


15.5 


.123 




11 


7. 


.123 




16 


22.5 


.124 


5 


14.4 


.124 




11 


4.81 


.124 




16 


19,22 


.125 


5 


13.33 


.125 




11 


2.66 


.125 




16 


16. 


.126 


5 


12.27 


.126 




11 


0.5 


.126 




16 


12.82 


.127 


5 


11.23 


.127 




10 


22.46 


.127 




16 


9.7 


.128 


5 


10.2 


.128 




10 


20.41 


.128 




16 


6.62 


.129 


5 


9.19 


.129 


I 


10 


18.39 


129 




16 


3.59 



168 EXAMPLES. 

The following will be the dividends, according to the number 
of yards for ascertaining the weight of any decimal part of a 
hank. 



Yards. 


Dividends. 


1 


8.333 


2 


16.666 


3 


25. 


4 


33.333 


5 


41.666 


6 


50. 


7 


58.333 


8 


66.666 


9 


75. 


10 


83.333 


15 


125. 


20 


166. 


30 


250. 


40 


333.333 


60 


500. 


80 


666.666 


120 


1000. 



RULE. — Divide the dividend by the hank, or decimal part of a 
hank, according to the number of yards weighed, and the quo- 
tient will be the weight in grains. 

What will 2 yards of 0.13 of a hank weigh? 
Dividend for 2 yards. 
13)16.666(128.2 grains, or 5 dwts., 8.2 grains, 
13 weight of 2 yards. 

36 

26 

106 
104 

26 
26 



CARDING AND DRAWING-TABLE. 



169 



CARDING AND DRAWING-TABLE. 

From .13 to .187 decimal of hank for 2, 4, and 6 yards. 



Dec. of 
hank. 


2 


yards. 


Dec. of 
hank. 


4 yards. 


| Dec. of 
1 hank. 


6 ya 


rds. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


I - 13 


5 


8.2 


.13 




10 


16.4 


.13 




16 


0.6 


I * 131 


5 


7.22 


.131 




10 


14.45 


.131 




15 


21.67 


I .132 


5 


6.26 


.132 




10 


12.5 


.132 




15 


18.781 


.133 


5 


5.31 


.133 




10 


10.62 


.133 




15 


15.93 1 


.134 


5 


4.37 


.134 




10 


8.75 


.134 




15 


13.13 | 


.135 


5 


3.45 


.135 




10 


6.91 


.135 




15 


10.37 


[ .136 


5 


2.55 


.136 




10 


5.2 


.136 




15 


7.74 


| .137 


5 


1.65 


.137 




10 


3.3 


.137 




15 


4.96 


.138 


5 


0.77 


.138 




10 


1.54 


.138 




15 


2,31 


I .139 


4 


23.9 


.139 




9 


23.8 


.139 




14 


23.7 


| -14 


4 


23. 


.14 




• 9 


22. 


.14 




14 


21. 1 
18.6 1 


.141 


4 


22.2 


.141 




9 


20.4 


.141 




14 


.142 


4 


21.37 


.142 




9 


18.74 


.142 




14 


16.11J 


1 - 143 


4 


20.55 


.143 




9 


17.1 


.143 




14 


13.65| 


1 - 144 


4 


19.74 


.144 




9 


15.48 


.144 




14 


11.22 
8.82 


.145 


4 


12.94 


.145 




9 


13.88 


.145 




14 


.146 


4 


18.15 


.146 




9 


12.31 


.146 




14 


6.46 1 
4.13 


.147 


4 


17.37 


.147 




9 


10.75 


.147 




14 


.148 


4 


16.61 


.148 




9 


9.22 


.148 




14 


1.83 


.149 


4 


15.85 


.149 




9 


7.71 


.149 




13 


23.57 


.15 


4 


15.11 


.15 




9 


6.22 


.15 




13 


21.33 | 


.151 


4 


14.37 


.151 




9 


4.75 


.151 




13 


19.12! 


.1525 


4 


13.29 


.1525 




9 


2.57 


.1525 




13 


15.861 


.153 


4 


12.93 


.153 




9 


1.86 


.153 




13 


14.79 I 


.155 


4 


11.52 


.155 




8 


23.05 


.155 




13 


10.58 I 


.157 


4 


10.15 


.157 




8 


20.31 


.157 




13 


6.47 


.1575 


4 


9.82 


.1575 




8 


19.6 


.1575 




13 


5.46 


.159 


4 


8.82 


.159 




8 


17.64 
16.33 


.159 




13 


2.46 J 


.16 


4 


8.16 


.16 




8 


.16 




13 


0.5 


.163 


4 


6.24 


.163 




8 


12.49 


.163 




12 


.18.74 S 


.165 


4 


5.1 


.165 




8 


10.2 


.165 




12 


15.3 | 


.167 


4 


3.8 


.167 




8 


7.6 


.167 




12 


11.4 S 


.17 


4 


2. 


.17 




8 


4. 


.17 




12 


6. 


.173 


4 


0.33 


.173 




8 


0.67 


.173 




12 


1.01 


.175 


3 


23.32 


.175 




7 


22.651 


.175 




11 


21.98 


.179 


3 


21.1 


.179 




7 


18.21 


.179 




11 


15.32 


.18 


3 


20.59 


.18 




7 


17.18 


.18 




11 


13.77 


.183 


3 


19.07 


.183 




7 


14.14 


.183 




11 


9.22 1 


.185 


3 


18.1 


.185 




7 


12.18 


.185 




11 


6.271 


.187 


3 


17.12 


.187 




7 


10.25 


.187 




11 


3.37! 

! 



12 



170 



EXAMPLES, 



What will 4 yards of 0.26 of a hank weigh? 

0.26)33.333(128.2 grains, or 5 dwts., 8.2 grains. 
26 



73 

52 



213 

208 



53 
52 



What will 6 yards of 0.335 of a hank weigh? 

0.335)50.000(149.25 grains, or 6 dwts. 5£- grains. 
335 



1650 
1340 

3100 
3015 



850 
670 

1800 
1675 

125 

If 6 yards of carding, or drawing weigh 6 dwts., 5j grains, 
what will the decimal of the hank be? 

6 dwts, 5i grs. = 149.25 grs.)50.0000(0.335 decimal of a hank, 

44775 and opposite which in 

the table under 6 yards 

52250 will be found 6 dwts. 
44775 5J- grains. 



74750 
74625 



125 



CARDING AND DRAWING-TABLE. 



171 



CARDING AND DRAWING-TABLE. 

From .19 to .31 decimal of hank for 2, 4, and 6 yards. 



1 Dec. of 
| hank. 


2 yards. 


Dec. of 


4 yards. 


Dec. of 

hank. 


6 yards. 


dwts. 


grains. 


hank. 


oz 


dwts. 


grains. 


oz 


dwts. 


grains. 


.19 


3 


15.71 


.19 




7 


7.43 


.19 




10 


23.15J 


.193 


3 


14.35 


.193 




7 


4.71 


.193 




10 


19.06 


.195 


3 


13.47 


.195 




7 


2.94 


.195 




10 


16.41 


.197 


3 


12.6 


.197 




7 


1.2 


.197 




10 


13.8 


•2 


3 


11.33 


.2 




6 


22.66 


.2 




10 


10. 


.203 


3 


10.09 


.203 




6 


20.2 


.203 




10 


6.3 


.205 


3 


9.3 


.205 




6 


18.6 


.205 


10 


3.9 


.207 


3 


8.51 


.207 




6 


17.03 


.207 




10 


1.54 


.21 


3 


7.36 


.21 




6 


14.73 


.21 




9 


22.1 


I * 213 


3 


6.24 


.213 




6 


12.49 


.213 




9 


18.74 


.215 


3 


5.51 


.215 




6 


11.03 


.215 




9 


16.551 


.217 


3 


4.8 


.217 




6 


9.6 


.217 




9 


14.41 


.22 


3 


3.75 


.22 




6 


7.51 


.22 




9 | 11.27 


.223 


3 


2.73 


.223 




6 


5.46 


.223 




9 


8.21 


.225 


3 


2.07 


.225 




6 


4.14 


.225 




9 


6.22 


.227 


3 


1.42 


.227 




6 


2.84 


.227 




9 


4.26 


.23 


3 


0.46 


.23 




6 


0.92 


.23 




9 


1.38 


.233 


2 


23.53 


.233 




5 


23.06 


.233 




8 


22.59 


.235 


2 


22.92 


.235 




5 


21.84 


.235 




8 


20.76 


.237 


2 


22.32 


.237 




5 


20.64 


.237 




8 


18.97 


.24 


2 


21.44 


.24 




5 


18.88 


.24 




8 


16.33 


.243 


2 


20.58 


.243 




5 


17.17 


.243 




8 


13.76 


.245 


2 


20.02 


.245 


5 


16.04 


.245 




8 


12.06 


.247 


2 


19.47 


.247 




5 


14.95 


.247 




8 


10.42 


.25 


2 


18.66 


.25 




5 


13.33 


.25 




8 


8. 


.253 


2 


17.87 


.253 




5 


11.75 


.253 




8 


5.62 


.255 


2 


17.36 


.255 




5 


10.71 


.255 




8 


4.07 


.257 


2 


16.85 


.257 




5 


9.7 


.257 




8 


2.55 I 


.26 


2 


16.1 


.26 




5 


8.2 


.26 




8 


0.3 


.263 


2 


15.37 


.263 




5 


6.74 


.263 




7 


22.11 


.265 


2 


14.89 


.265 




5 


5.78 


.265 




7 


20.671 


.27 


2 


13.72 


.27 




5 


3.45 


.27 




7 


17.183 


.275 


2 


12.6 


.275 




5 


1.21 


.275 




7 


13.811 


.28 


2 


11.52 


.28 




4 


23.04 


.28 




7 


10.56S 


.285 


2 


10.47 


.285 




4 


20.95 


.285 




7 


7.43 1 


.29 


2 


9.47 


.29 




4 


18.94 


.29 




7 


4.41 J 


.295 


2 


8.49 


.295 




4 


16.99 


.295 




7 


1.49g 


.3 


2 


7.55 


.3 




4 


15.11 


.3 




6 


22.66| 


.305 


2 


6.64 


.305 




4 


13.28 


.305 




6 


19.93J 


.31 


2 


5.76 


.31 




4 


11.52 


.31 




6 


17.281 



172 EXAMPLES. 

Suppose 2 yards of carding, or drawing weigh 2 dwts., 20 
grains, or 68 grains; what proportion of a hank will it be ? Thus 
2 yards is q\ of a lea, which is equal to 16.666 grains, which 
must be divided by the weight 2 yards, which is 68 grains. 
2 dwts., 20 grains, = 68 grns.)16.666(.245 decimal, or proportion 

136 of a hank. 



306 

272 



346 
340 



What will 6 yards of 0.4 hank drawing weigh ? 
0.4)50.00 



125 grains, or 5 dwts., 5 grains. 

If 6 yards of carding, or drawing weigh 5 dwts., 5 grains ; 
what proportion of a hank will it be ? 

5 dwts., 5 grains, = 125 grains,)50. 000(0.4 proportion of hank. 

500 

What will 3 yards of 0.7 hank carding, or drawing weigh ? 
Decimal of a hank, 0.7)25.00 



1 dwt., is 24 grns.)35.71(l dwt., 11.7 grains weight. 
24 



11.71 



What will 4 yards of 0.7 hank carding, or drawing weigh ? 
Decimal of hank 0.7)33.333 



24)47.619(1 dwt., 23.6 grains weight. 
24 

23.6 



CARDING AND DRAWING-TABLE. 



173 



CARDING AND DRAWING-TABLE. 
From .315 to .95 decimal of hank for 2, 4, and 6 yards. 



Dec. of 
hank. 


2 yards. 


d r 

Dec. of 
hank. 


4 yards. 


1 
Dec. of 

hank. 


6 yards. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


.315 


2 


4.91 


.315 




4 


9.82 


.315 




6 


14.73 


.32 


2 


4.08 


.32 




4 


8.16 


.32 




6 


12.24 


.325 


2 


3.28 


.325 




4 


6.56 


.325 




6 


9.84 


.33 


2 


2.5 


.33 




4 


5.01 


.33 




6 


7.51 


.335 


2 


1.75 


.335 




4 


3.5 


.335 




6 


5.25 


.34 


2 


1. 


.34 




4 


2. 


.34 




6 


3. 


.345 


2 


0.3 


.345 




4 


0.61 


.345 
.35 


6 


0.92 


.35 




23.61 


.35 




3 


23.23 


5 


22.85 


.355 




22.94 


.355 




3 


21.89 


.355 




5 


20.94 


.36 




22.29 


.36 




3 


20.59 


.36 




5 


18.88 


.365 




21.66 


.365 




3 


19.22 


.365 




5 


16.98 


.37 




21.04 


.37 




3 


18.09 


.37 




5 


15.13 


.375 




20.44 


.375 




3 


16.88 


.375 




5 


13.32 


.38 




19.86 


.38 




3 


15.71 


.38 




5 


11.58 


.385 




19.29 


.385 




3 


14.58 


.385 




5 


9.87 


.39 




18.73 


.39 




3 


13.47 


.39 




5 


8.2 


.395 




18.19 


.395 




3 


12.38 


.395 




5 


6.58 


.4 




17.66 


.4 




3 


11.33 


.4 




5 


5. 


.41 




16.65 


.41 




3 


9.3 


.41 




5 


1.95 


.42 




15.68 


.42 




3 


7.36 


.42 




4 


23.05 


.43 




14.75 


.43 




3 


5.51 


.43 




4 


20.28 


.44 




13.87 


.44 




3 


3.75 


.44 




4 


17.63 


.45 




13.03 


.45 




3 


2.07 


.45 




4 


15.11 


.46 




12.23 


.46 




3 


0.46 


.46 




4 


12.69 


.47 




11.46 


.47 




2 


22.92 


.47 




4 


10.38 


.48 




10.72 


.48 




2 


21.44 


.48 




4 


8.16 


.49 




10.01 


.49 




2 


20.02 


.49 




4 


6.04 


.5 




9.33 


.5 




2 


18.66 


.5 




4 


4. 


.52 




8.05 


.52 




2 


16.1 


.52 




4 


0.15 

20.59 
17.28 


.54 




6.86 


.54 




2 


13.72 


.54 




3 


.56 




5.76 


.56 




2 


11.52 


.56 




3 


.58 




4.73 


.58 




2 


9.47 


.58 




3 


14.2 


.6 




3.77 


.6 




2 


7.55 


.6 




3 


11.33 


.65 




1.64 


.65 




2 


3.28 


.65 




3 


4.92 


.7 




23.8 


.7 






23.6 


.7 




2 


23.42 


.75 




22.22 


.75 






20.44 
17.66 


.75 




2 


18.66 


.8 




20.83 


.8 






.8 


2 


14.5 


.85 




19.6 


.85 






15.21 


.85 




2 


10.82 


.9 




18.51 


.9 






13.04 


.9 




2 


7.55 


.95 




17.54 


.95 






11.08 


.95 




2 


4.62 



174 EXAMPLES. 

If 8 yards of drawing weigh 1 oz., 7 dwts., 0.5 grains; what 
decimal part of a hank will it be? 

Then 18 dwts. 5J grains troy is equal to 1 oz. avoirdupois; 
therefore 1 oz., 7 dwts., 0.5 grains will be equal to 25 dwts., 6 
grains troy, or 606 grains, which will be the divisor, and 8 yards 
which is y^ of a lea, or 66.666 grains, will be the dividend. 

606 grains,)66. 666(0. 11 decimal of a hank. 
606 



606 
606 



If 10 yards of carding, or drawing weigh 1 oz., 12 dwts., 18.5 
grains ; what decimal of a hank will it be ? 

Grains. 
1 ounce = 437.5 
12 dwts. = 288 

18.5 



744 grains, in 1 oz., 12 dwts., 18J grains. 

744 grains,)83.333(0.112 decimal of a hank. 

744 

893 
744 

1493 
1488 



EXAMPLES. 175 

What will 8 yards of 0.112 of a hank drawing weigh? 

Dividend. 
0.112)66.666(595.2 grains. 
560 



1066 

1008 



586 
560 

266 

224 

42 

1 oz. is 437.5 grs.)595.2(l oz. 
437.5 



1 dwt. is 24 grs.)157.7(6 dwts. 
144 



13.7 grains. 

OR, 

1 oz. 6 dwts., 13.7 grains. 



176 



CARDING AND DRAWING-TABLE. 



CARDING AND DRAWING-TABLE. 
From .066 to .11 decimal of hank for 8 and 10 yards. 



| Dec. of 
1 hank. 


1 8 yards. 


Dec. of 

hank. 




10 yards. 


oz. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


.066 


2 


5 


15.1 


.066 


2 


16 


3.6 


.067 


2 


5 


0. 


.067 


2 


15 


8.7 


| .068 


2 


4 


9.4 


.068 


2 


14 


14.4 


I '° 69 


2 


3 


19.1 


.069 


2 


13 


20.7 


.07 


2 


3 


5.3 


.07 


2 


13 


3.3 


I .071 


2 


2 


15.9 


.071 


2 


12 


10.7 


I - 072 


2 


2 


2.9 


.072 


2 


11 


18.4 


.073 


2 


1 


14.2 


.073 


2 


11 


2.5 


.074 


2 


1 


2. 


.074 


2 


10 


11.1 


.075 


2 





13.8 


.075 


2 


9 


20.1 


.076 


2 





2.2 


.076 


2 


9 


5.4 


.077 




17 


20.3 


.077 


2 


8 


15.2 


.078 




17 


9.2 


.078 


2 


8 


1.3 


.079 




16 


22.3 


.079 


2 


7 


11.8 


.08 




16 


11.8 


.08 


2 


6 


22.6 


.081 




16 


1.5 


.081 


2 


6 


9.8 


.082 




15 


15.5 


.082 


2 


5 


21.2 


.083 




15 


5.7 


.083 


2 


5 


9. 


.084 




14 


20.1 


.084 


2 


4 


21. 


.085 




14 


10.8 


.085 


2 


4 


9.3 


.086 




14 


1.6 


.086 


2 


3 


21.8 


.087 




13 


16.7 


.087 


2 


3 


10.9 


.088 




13 


8. 


.088 


2 


2 


23.3 


.089 




12 


23.5 


.089 


2 


2 


13.2 


.09 




12 


15.2 


.09 


2 


2 


2.7 


.091 




12 


7.1 


.091 


2 


1 


16.7 


.092 




11 


23.1 


.092 


2 


1 


6.3 


.093 




11 


15.3 


.093 


2 





21. 


.094 




11 


7.7 


.094 


2 





11.5 


.095 




11 


0.2 


.095 


2 





2.1 


.096 




10 


16.9 


.096 




17 


22.5 


.097 




10 


9.7 


.097 




17 


13.6 


.098 




10 


2.7 


.098 




17 


4.8 


.099 




9 


19.9 


.099 




16 


20.2 


.1 




.9 


13.1 


.1 




16 


11.8 


.102 




9 


0. 


.102 




15 


19.4 


.104 




8 


11.5 


.104 




15 


3.7 


.106 




7 


23.4 


.106 




14 


12.6 


.108 




7 


11.7 


.108 




13 


22.1 


.11 




7 


0.5 


.11 




13 


.. | 



EXAMPLES. 



177 



When the proportion or decimal of the hank is found, the fol- 
lowing table will show the dividend for any number of inches in 
length, from 1 to 36 inches, when the quotient will be the weight 
in grains: — 



nches. 


Dividends. 


Inches. 


Dividends 


1 


.23148 


19 


4.39812 


2 


.46296 


20 


4.6296 


3 


.69444 


21 


4.86108 


4 


.92592 


22 


5.09256 


5 


1.15740 


23 


5.32404 


6 


1.38888 


24 


0.55555 


7 


1.62036 


25 


5.787 


8 


1.85184 


26 


6.01848 


9 


2.08332 


27 


6.24996 


10 


2.3148 


28 


6.48144 


11 


2.54628 


29 


6.71292 


12 


2.77777 


30 


6.9444 


13 


3.00924 


31 


7.17588 


14 


3.24072 


32 


7.40736 


15 


3.4722 


33 


7.63884 


16 


3.70368 


34 


7.87032 


17 


3.93516 


35 


8.1018 


18 


4.16666 


36 


8.3333 



IF. B. — The above tables will show the dividends for any number 
of inches of lap, or cotton fed on feed-cloth at lap machine ; 
the quotient of which will be the weight in grains ; the divisor 
must be invariably the decimal, or proportion of the hank. 

If the decimal, or proportion of the hank at the lap machine, 
according to the draught and doubling, be 0.0005; what weight 
of cotton must be fed on 12 inches of feed-cloth at lap machine? 

Thus— Dec. of hank, 0.0005)2.7777 dividend for 12 inches. 



5555.5 grains, or 12 oz., 12 dwts., 
17J- grains, the weight of 
cotton required. 

N. B. — The loss sustained in working must be added to the net 
weight according to the number of hanks produced. 



178 



CARDING AND DRAWING-TABLE. 



CARDING AND DR A WING-TABLE. 
From .112 to .24 decimal of hank for 8 and 10 yards. 



Dec. of 
hank. 




8 yards. 


Dec. of 
hank. 


10 yards. 


oz. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


.112 


1 


6 


13.7 


.112 


1 


12 


18.5 


.114 


1 


6 


3.2 


.114 


1 


12 


5.4 


.116 


1 


5 


17.2 


.116 


1 


11 


16.8 


.118 


1 


5 


7.4 


.118 


1 


11 


4.7 


.12 


1 


4 


22. 


.12 


1 


10 


16.6 


.122 


1 


4 


12.9 


.122 


1 


10 


5.5 


.124 


1 


4 


4.2 


.124 


1 


9 


18.5 


.126 


1 


3 


19.6 


.126 


1 


9 


7.8 


.128 


1 


3 


11.3 


.128 


1 


8 


21.5 


.13 


1 


3 


3.3 


.13 


1 


8 


11.5 


.132 


1 


2 


19.5 


.132 


1 


8 


1.8 


.134 


1 


2 


12. 


.134 


1 


7 


15.6 


.136 


1 


2 


4.6 


.136 


1 


7 


7.2 


.138 


1 


1 


21.5 


.138 


1 


6 


22.3 


.14 


1 


1 


14.6 


.14 


1 


6 


13.7 


.142 


1 


1 


7.9 


.142 


1 


6 


5.3 


.144 


1 


1 


0.7 


.144 


1 


5 


21.2 


.146 

.148 


1 





19.1 


.146 


1 


5 


12.6 


1 





12.9 


.148 


1 


5 


6. 


.15 


1 





6.9 


.15 


1 


4 


22. 


.1525 




18 


5.1 


.1525 


1 


4 


12.9 


.155 




17 


22.1 


.155 


1 


4 


4.1 


.1575 




17 


15.2 


.1575 


1 


3 


19.6 


.16 




17 


8.6 


.16 


1 


3 


11.3 


.165 




16 


20. 


.165 


1 


2 


19.5 


.17 




16 


8.1 


.17 


1 


2 


4.5 


.175 




15 


20.9 


.175 


1 


1 


14.6 


.18 




15 


10. 


.18 


1 


1 


1.4 


.185 




15 


0.3 


.185 


1 





12.9 


.19 




14 


14.8 


.19 


1 





1.1 


.195 




14 


5.8 


.195 




17 


19.3 


.2 




13 


21.3 


.2 




17 


8.6 


.205 




13 


13.2 


.205 




16 


22.5 


.21 




13 


5.4 


.21 




16 


12.8 


.215 




12 


22. 


.215 




16 


3.5 


.22 




12 


15. 


.22 




15 


18.7 


.225 




12 


8.2 


.225 




15 


10.3 


1 « 23 




12 


1.8 


.23 




15 


2.3 


1 .235 




11 


19.6 


.235 




14 


18.6 


1 .24 




11 


13.7 


.24 




14 


11.2 



EXAMPLES. 179 

If 8 yards of carding, or drawing weigh 16 dwts., 20 grains; 
what proportion, or size of hank will it be ? 

Then 16 dwts., 20 grains are equal to 404 grains, which will 
be the divisor; and 8 yards are ^ of a lea, or 66.666 grains, 
which will be the dividend. 

404)66.666(0.165 decimal, or proportion of hank, 
404 opposite to which in the table 

under 8 yards, is 16 dwts., 20 

2626 grains, the weight. 

2424 



2026 
2020 



6 

If 8 yards of carding or drawing weigh 4 dwts., 5 grains ; 
what proportion, or size of hank will it be? 

4 dwts., 5 grs, are equal to 101 grs.)66. 666(0. 66 proportion, or 

606 size of hank. 



606 
606 



What will 8 yards of 0.165 of a hank of carding, or drawing 
weigh ? 

Then 8 yards are T \ of a lea, which is equal to 66.666 grains, 
which will be the dividend, and the decimal of the hank 0.165 
the divisor. 

0.165)66.666(404 grains, or 16 dwts., 20 grains, which 

660 will be found in the column under 8 

yards; to the left hand of which will 

666 be found 0.165, which is the decimal, 

660 or size of a hank for 8 yards of card- 

ing or drawing that weighs 16 dwts. 

6 20 grains. 



180 



CARDING AND DRAWING-TABLE. 



CAKDING AND DE A WING-TABLE. 

From .245 to .48 decimal of hank for 8 and 10 yards. 



Dec. of 
hank. 


8 yards. 


Dec. of 
hank. 


10 yards. 


oz. 


dwts. 


grains. 


oz. 


dwts. 1 


grains. 


.245 




11 


8.1 


.245 




14 


4. 


.25 




11 


2.6 


.25 




13 


21.3 


.255 




10 


21.4 


.255 




13 


14.7 


.26 




10 


16.4 


.26 




13 


8.5 


.265 




10 


11.5 


.265 




13 


2.4 


.27 




10 


6.9 


.27 




12 


20.6 


.275 




10 


2.4 


.275 




12 


15. 


.28 




9 


22. 


.28 




12 


9.6 


.285 




9 


17.9 


.285 




12 


4.3 


.29 




9 


13.8 


.29 




11 


23.3 


.295 




9 


9.9 


.295 




11 


18.4 


.3 




9 


6.2 


.3 




11 


13.7 


.305 




9 


2.5 


.305 




11 


9.2 


.31 




8 


23. 


.31 




11 


4.8 


.315 




8 


19.6 


.315 




11 


0.5 


.32 




8 


16.3 


.32 




10 


20.4 


.325 




8 


13.1 


.325 




10 


16.4 


.33 




8 


10. 


.33 




10 


12.5 


.335 




8 


7. 


.335 




10 


8.7 


.34 




8 


4. 


.34 




10 


5. 


.345 




8 


1.2 


.345 




10 


1.5 


.35 
.355 




7 


22.4 


.35 




9 


22. 




7 


19.7 


.355 




9 


18.7 


.36 




7 


17.1 


.36 




9 


15.4 


.365 




7 


14.6 


.365 




9 


12.3 


.37 




7 


12.1 


.37 




9 


9.2 


.375 




7 


9.7 


.375 




9 


6.2 


.38 




7 


7.4 


.38 




9 


3.3 


.385 




7 


5.1 


.385 




9 


0.4 


.39 




7 


2.9 


.39 




8 


21.6 


.395 




7 


0.7 


r 




8 


18.9 


.4 




6 


22.6 




8 


16.3 


.41 




6 


18.6 


.41 




8 


11.2 


.42 




6 


14.7 


.42 




8 


6.4 


.43 




6 


11. 


.43 




8 


1.8 


.44 




6 


7.5 


.44 




7 


21.3 


.45 




6 


4.1 


.45 




7 


17.1 


.46 




6 


0.9 


.46 




7 


13.1 


.47 




5 


21.8 


.47 




7 


9.3 


.48 




5 


18.8 


.48 




7 


5.6 



EXAMPLES. 181 

What will 18 yards of 1J hank slabbing weigh? 

Then 18 yards is 2 3 q of a lea, or 120 yards, which is equal to 
150 grains of a 1 hank, which, divided by 1J, or 1.25, will give 
the weight in grains that 18 yards should weigh. 

Grains. 
Hank slabbing 1.25)150.0(120 grains, or 5 dwts., weight 
125 required. 



250 
250 



If 18 yards of slabbing weigh 5 dwts., or 120 grains ; what 
hank will it be? 

120)150.00(1.25 hank slabbing. 
120 



300 
240 



600 
600 

What will 37 yards of If hank slabbing weigh? 

Then 37 yards is y 3 ^ of a lea, or 120 yards, which is equal to 
308.333 grains of a 1 hank, which, divided by If, or 1.75, will 
give the weight in grains that 37 yards should weigh. 

1.75)308.3333(176.19 grains, or 7 dwts., 8.19 
175 grs., weight required, 

1333 

1225 

1083 
1050 

333 
175 

1583 
1575 



182 



CARDING, DRAWING, AND SLABBING-TABLE. 



CARDING-, DRAWING, AND SLABBING-TABLE. 
From .5 to .99 decimal of hank for 8, 10, and 20 yards. 



1 Dec. of 

I hank. 


8 


yards. 


Dec. of 


10 yards. 


| Dec. of 


20 yards. 


[dwts. 


grains. 


hank. 


oz. 


dwts 


grains. 


1 hank. 


oz 


dwts. 


grains. 


•5 


1 5 


13.3 


.5 


6 


22.6 


.5 


13 


21.2 


.51 


5 


10.7 


.51 


6 


19.4 


.51 


13 


14.8 


.52 


5 


8.2 


.52 


6 


16.2 


.52 




13 


8.4 


.53 


5 


5.7 


.53 


6 


13.2 


.53 




13 


2.4 


.54 


5 


3.4 


.54 


6 


10.3 


.54 




12 


20.6 


.55 


5 


1.2 


.55 


6 


7.5 


.55 




12 


15. 


.56 


4 


23. 


.56 


6 


4.8 


•56 | 


12 


9.6 


.57 


4 


20.9 


.57 


6 


2.2 


.57 




12 


4.4 


.58 


4 


18.9 


.58 


5 


23.6 


.58 




11 


23.2 


.59 


4 


17. 


.59 


5 


21.2 


.59 




11 


18.4 


.6 


4 


15.1 


.6 


5 


18.8 


.6 




11 


13.6 


.62 


4 


11.5 


.62 


5 


14.4 


.62 




11 


4.8 


.64 


4 


8.1 


.64 


5 


10.2 


.64 




10 


20.4 


.66 


4 


5. 


.66 


5 


6. 


.66 




10 


12. 


.68 


4 


2. 


.68 


5 


2.5 


.68 




10 


5. 


.7 


3 


23.2 


.7 




4 


23. 


.7 




9 


22. 


.72 


3 


20.6 


.72 




4 


19.6 


.72 




9 


15.2 


.74 


3 


18. 


.74 




4 


16.6 


.74 




9 


9.2 


1 - 76 


3 


15.7 


.76 




4 


13.6 


.76 




9 


3.2 


.78 


3 


13.4 


.78 




4 


10.8 


.78 




8 


21.6 


.8 


3 


11.3 i 


.8 




4 


8.1 


.8 




8 


16.2 


.81 


3 


10.3 


.81 




4 


6.8 


.81 




8 


13.7 


.82 


3 


9.3 


.82 




4 


5.6 


.82 




8 


11.2 


.83 


3 


8.2 


.83 




4 


4.3 


.83 




8 


8.8 


.84 


3 


7.3 


.84 




4 


3.2 


.84 




8 


6.4 


.85 


3 


6.4 


.85 




4 


2. 


.85 




8 


4. 


.86 


3 


5.5 


.86 




4 


0.9 


.86 




8 


1.8 


.87 


3 


4.6 


.87 




3 


23.7 


.87 j 




7 


23.5 


.88 


3 


3.7 


.88 




Q 
O 


22.7 


.88 




7 


21.4 


.89 


3 


2.9 


.89 




3 


21.6 


.89 




7 


19.2 


.9 


3 


2. 


.9 




3 


20.6 


.9 




7 


17.2 


.91 


3 


1.2 


.91 




3 


19.5 


.91 




7 


15.1 


.92 


3 


0.4 


.92 




3 


18.6 


.92 




7 


13.2 


.93 


3 


23.6 


.93 




3 


17.5 


.93 




7 


11.2 


.94 


2 


23. 


.94 




3 


16.6 


.94 




7 


9.2 


.95 


2 


22.1 J 


.95 




3 


15.6 


.95 




7 


7.3 


.96 


2 


21.4 


.96 1 




3 


14.8 


.96 




7 


5.6 


.97 


2 


20.7 


.97 




3 


13.9 


.97 




7 


3.8 


.98 


2 


20. 


.98 




3 


13. 


.98 




7 


2. 


.99 


2 


19.3 J 


.99 




3 


12.1 


.99 




7 


0.3 



EXAMPLES. 183 

. The slabbing and roving tables rise progressively in 20th parts 
of a hank, as will be seen in the following tables. Thus 1, 1.05, 
or I^q and so on to 2 and 3 hank, &c. 

What will 20 yards of 1J, or 1.25 hank slabbing weigh? 

Then 20 yards is J of a lea, or 120 yards, which is equal to 
166.66 grains of a 1 hank, as shown in a preceding table; which, 
divided by 1J, or 1.25, will give the weight in grains that 20 
yards should weigh. 

Grains. 
Hank slabbing, 1.25)166.66(133.33, or 5 dwts. 1S T % grs. weight, 
125 which will be found in the 

table opposite 1.25, and 



416 under 20 yards 

375 



416 
375 



416 
375 

416 
375 

41 

If 20 yards of slabbing weigh 5 dwts., 13.3 grains; what hank 
Will it be? 

5 dwts., 13.3 grains = 133,33)166.66(1.25, or 1J hank slabbing. 

13333 



33336 

26666 



66706 
66666 

40 



184 



SLABBING AND ROVING-TABLE. 



SLABBING AND ROVING-TABLE. 
From 1 hank to 2.95 hanks for 20, 30, 40, and 60 yards 



Hank 1 

roving. | 


20 


yards. 30 yards. 


40 yards. 


1 

60 yards. 


dwts. 


grains, jjoz. 


dwts. 


grains. 1 


dwts. 


grains. 


oz. 


dwts. 


grains. 


1. ( 


6 


22.6 | 


10 


10. 


13 


21.3 


1 


2 


14.5 


1.05 


6 


14.7 




9 


22. 1 


13 


5.4 


1 


1 


14.7 


1.1 


6 


7.5 




9 


11.2 | 


12 


15. 


1 





17. 


1.15 


6 


0.9 




9 


1.3 


12 


1.8 




18 


2.7 


1.2 


5 


18.8 




8 


16.3 


11 


13.7 




17 


8.6 


1.25 


5 


13.3 




8 


8. 


11 


2.6 




16 


16. 


1.3 


5 


8.2 




8 


0.3 1 


10 


16.4 




16 


0.6 


1.35 


5 


3.4 




7 


17.1 


10 


6.9 




15 


10.3 


1.4 


4 


23. 




7 


10.5 1 


9 


22. 




14 


21.1 


1.45 


4 


18.9 




7 


4.4 


9 


13.8 




14 


8.8 


1.5 


4 


15.1 




6 


22.6 


9 


6.2 




13 


21.3 


1.55 


4 


11.5 




6 


17.2 


8 


23. 




13 


10.5 


1.6 


4 


8.1 




6 


12.2 


8 


16.3 




13 


0.5 


1.65 


4 


5.1 




6 


7.6 


8 


10.2 




12 


15. 


1.7 


4 


2. 




6 


3. 


8 


4. 




12 


6.1 


1.75 


3 


23.9 


5 


22.8 


7 


22.4 




11 


21.7 


1.8 


3 


20.6 




5 


18.8 


7 


17.1 




11 


13.7 


1.85 


3 


18. 




5 


15.1 


7 


12.1 




11 


6.2 


1.9 


3 


15.7 




5 


11.5 


7 


7.4 




10 


23.1 


1.95 


3 


13.4 




5 


8.2 


7 


2.9 




10 


16.4 


2. 


3 


11.3 




5 


5. 


6 


22.6 




10 


10. 


2.05 


3 


9.3 




5 


1.9 


6 


18.6 




10 


3.8 


2.1 


3 


7.3 




4 


23. 


6 


14.7 




9 


22. 


2.15 


3 


5.5 




4 


20.2 


. 6 


11. 




9 


16.4 


2.2 


3 


3.7 


4 


17.6 


6 


7.5 




9 


11.3 


2.25 


3 


2. 


4 


15.1 


6 


4.1 




9 


6.2 


2.3 


3 


0.4 


4 


12.6 


6 


0.9 




9 


1.3 


2.35 


2 


22.9 


4 


10.3 


5 


21.8 




8 


10.6 


2.4 


2 


21.4 


4 


8.1 


5 


18.8 


8 


16.2 


2.45 


2 


20. 


4 


6. 


5 


16. 


8 


12. 


2.5 


2 


18.6 




4 


4. 


5 


13.3 


8 


8. 


2.55 


2 


17.3 




4 


2. 


5 


10.7 


8 


4. 


2.6 


2 


16.1 




4 


0.1 


5 


8.2 


8 


0.3 


2.65 


2 


14.9 




3 


22.3 


5 


5.7 


7 


20.6 


2.7 


2 


13.7 




3 


20.6 


5 


3.4 


7 


17.2 


2.75 


2 


12.6 




3 


18.9 


5 


1.2 


7 


13.8 


2.8 


i 2 


11.5 | 


3 


17.2 


4 


23. 


7 


10.5 


2.85 


2 


10.4 




3 


15.7 


4 


20.9 




7 


7.4 


2.9 


2 


9.4 




3 


14.2 


4 


18.9 




4.4 


2.95 


1 2 


8.5 




3 


12.7 


4 


17. 




7 


1.5 



EXAMPLES. 185 

What will 30 yards of 2 T 9 ^ hank roving weigh? 

250 is the dividend for 30 yards, which must be divided by the 
hank roving, and the quotient will be the weight in grains. 

Hank roving, 2.9)250(86.2 grains, or 3 dwts., 14.2 grs., which 
232 will be found in the table under 30 
yards, and opposite 2.9 in the co- 

180 lumn of the hank roving. 

174 



60 

58 



If 40 yards weigh 4 dwts., 5 grains; what hank-roving will 
it be? 

4 dwts., 5 grains, = 101 grs.)333.33(3.3, or 3 t 3 q hank-roving. 

303 

303 
303 

What will 60 yards of 3f, or 3.75 hank-roving weigh? 

500 is the dividend for 60 yards. 

Hank-roving 3}, or 3.75)500.00(133.3, or 5 dwts., 13.3 grs. 

375 weightof 60 yards of 

a 3| hank-roving. 

1250 
1125 

1250 
1125 

1250 
1125 

• 125 

13 



186 



ROVING-TABLE. 



ROVING-TABLE. 

From 3 hank, to 7.25 hanks, for 20, 30, 40, and 60 yards. 



Hank 
roving. 


20 yards. 


30 yards. 


40 yards. 


1 

60 yards. 


dwts 


grains. 


dwts 


grains. 


I dwts 


grains. 


dwts 


grains. 


3. 


2 


7.5 


3 


11.3 


4 


15.1 


6 


22.6 


3.05 


2 


Q.6 


3 


9.9 


4 


13.2 


6 


19.9 


3.1 


2 


5.7 


3 


8.6 


4 


11.5 


6 


16.3 


3.15 


2 


4.9 


3 


7.3 


4 


9.8 


6 


14.7 


3.2 


2 


4. 


3 


6.1 


4 


8.1 


6 


12.2 


3.25 


2 


3.2 


3 


4.9 


4 


6.5 


6 


9.8 


3.3 


2 


2.5 


3 


3.7 


4 


5. 


6 


7.5 


3.35 


2 


1.7 


3 


2.6 


4 


3.5 


6 


5.2 


3.4 


2 


1. 


3 


1.5 


4 


2. 


6 


3. 


3.45 


2 


0.3 


3 


0.4 


4 


0.6 


6 


0.9 


3.5 




23.6 


2 


23.4 


3 


22.2 


5 


22.8 


3.55 




22.9 


2 


22.4 


3 


21.9 


5 


20.8 


3.6 




22.3 


2 


21.4 


3 


20.6 


5 


18.8 


3.65 




21.6 


2 


20.5 


3 


19.3 


5 


16.9 


3.7 




21. 


2 


19.5 


3 


18.1 


5 


15.1 


3.75 




20.4 


2 


18.6 


3 


16.8 


5 


13.3 


3.8 




19.8 


2 


17.7 


3 


15.7 


5 


11.5 


3.85 




19.2 


2 


16.9 


3 


14.5 


5 


9.9 


3.9 




18.7 


o 


16.1 


3 


13.4 


5 


8.2 


3.95 




18.1 


2 


15.3 


3 


12.4 


5 


6.6 


4. 




17.6 


2 


14.5 


3 


11.3 


5 


5. 


4.1 




16.6 


2 


12.9 


3 


9.3 


5 


1.9 


4.2 




15.7 


2 


11.5 


*3 


7.3 


4 


23. 


4.3 




14.7 


2 


10.1 


3 


5.5 


4 


20.2 


4.4 




13.8 


2 


8.8 


3 


3.7 


4 


17.6 


4.5 




13. 


2 


7.5 


3 


2. 


4 


15.1 


4.6 




12.2 


2 


6.3 


3 


0.4 


4 


12.7 


4.7 




11.4 


2 


5.2 


2 


22.9 


4 


10.4 


4.8 




10.7 


2 


4.1 


2 


21.4 


4 


8.1 


4.9 




10. 


2 


3. 


2 


20: 


4 


6. 


5. 




9.3 


2 


2. 


2 


18.6 


4 


4. 


5.25 




7.6 




23.6 


2 


15.2 


3 


23.2 


5.5 




6.3 




21.4 


2 


12.6 


3 


18.9 


5.75 




4.9 




19.5 


2 


9.9 


3 


15. 


6. 




3.7 




17.6 


2 


7.5 


3 


11.3 


6.25 




2.6 




16. 


2 


5.3 


3 


8. 


1 6.5 




1.6 




14.4 


2 


3.2 


3 


4.9 


6.75 




0.6 




13. 


2 


1.3 


3 


2. 


7. 




23.8 




11.7 


1 


23.6 


2 


23.4 


7.25 




22.9 




10.4 


1 


21.9 


2 


20.9 



ROVING-FRAME. 187 

CHANGE-PINIONS AT ROVING-FRAME. 

By changing the driving-wheels, less pinions produce finer 
roving, by increasing the draught in rollers : driven-wheels de- 
crease the hank-roving by reducing the draught in the rollers. 
RULE. — Multiply the hank-roving by the number of teeth in the 
change-wheel, or pinion, and divide by the hank-roving you 
want, and the quotient will be the change-wheel, or pinion re- 
quired. 

If a 4 hank-roving requires a 24 teeth change-wheel, or pinion ; 
what will a 4} hank require? 

4 hank-roving. 
24 teeth, change-wheel, or pinion. 



Hank-rov. required, 4.75)96.00(20.21, or 20 teeth, change-pinion, 

9500 being a driving-wheel. 

1000 
950 



500 

475 

25 

If a 4 hank-roving requires a 48 teeth (driven) change-wheel, 
or pinion ; what will a 4 \ hank require ? 

4 hank-roving. 
48 teeth, change-wheel. 



Hank-rov. required, 4.25)192.00(45.17, or 45 teeth, change-whl. 

1700 or pinion required, being 



a driven- wheel. 



2200 
2125 

750 

425 



3250 
2975 

275 



2V*. B.—~It seldom occurs that a change-wheel can he had to pro- 
duce exactly what is wanted. 



188 



ROVING-TABLE. 



ROVING-TABLE. 

From 7.5 to 18.5 hanks for 30, 40, 60, and 120 yards. 



Dec. of 
hank. 


30 yards. 


40 


yards. 


. 1 

60 yards. f 120 yards 


or 1 lea.i 


dwts. 


grains. 


dwts. 


grains. 


oz. 


dwts. 


grains. |oz. 


dwts. 


grains. | 


7.5 


1 


9.3 


1 


20.4 




2 


18.6 




5 


13.3 


7.75 


1 


8.2 


1 


19. 




2 


16.5 




5 


9. 


8. 


1 


7.2 


1 


17.6 




2 


14.5 




5 


5. 


8.25 


1 


6.3 


1 


16.4 




2 


12.6 




5 


1.2 


8.5 


1 


5.4 


1 


15.2 




2 


10.8 




4 


21.6 


8.75 


1 


4.5 


1 


14.1 




2 


9.1 




4 


18.2 


9. 


1 


3.7 


1 


13. 




2 


7.5 




4 


15.1 


9.25 


1 


3. 


1 


12. 




2 


6. 




4 


12. 


9.5 


1 


2.3 


1 


11.1 




2 


4.6 




4 


9.2 


9.75 


1 


1.6 


1 


10.1 




2 


3.2 




4 


6.4 


10. 


1 


1. 


1 


9.33 




2 


2. 




4 


4. 


10.25 


1 


0.39 


1 


8.52 




2 


0.78 




4 


1.56 


10.5 




23.81 


1 


7.73 




1 


23.62 




3 


23.23 


10.75 




23.26 


1 


7. 




1 


22.52 




3 


21.04 


11. 




22.72 


1 


6.3 




1 


22.15 




3 


18.9 


11.25 




22.22 


1 


5.62 




1 


20.44 




3 


16.88 


11.5 




21.73 


1 


4.98 




1 


19.47 




3 


14.95 


11.75 




21.27 


1 


4.33 




1 


18.55 




3 


13.1 


12. 




20.83 


1 


3.77 




1 


17.66 




3 


11.33 


12.25 




20.4 


1 


3.2 




1 


16.81 




3 


9.6 


12.5 




20. 


1 


2.66 




1 


16. 




3 


8. 


12.75 




19.6 


1 


2.14 




1 


15.21 




3 


6.43 


13. 




19.23 


1 


1.64 




1 


14.46 




3 


4.92 


13.25 




18.86 


1 


1.16 




1 


13.73 




3 


3.47 


13.5 




18.51 


1 


0.69 




1 


13.03 




3 


2.07 


13.75 




18.18 


1 


0.24 




1 


12.36 




3 


0.72 


14. 




17.85 




23.8 




1 


11.71 




2 


23.42 


14.25 




17.54 




23.39 


1 


11.08 




2 


22.17 


14.5 




17.24 




22.98 




1 


10.48 




2 


20.96 


14.75 




16.94 




22.89 




1 


9.89 




2 


19.79 


15. 




16.66 




22.22 




1 


9.33 




2 


18.66 


15.25 




16.39 




21.85 




1 


8.78 




2 


17.57 


15.5 




16.12 




21.52 




1 


8.25 




2 


16.57 


15.75 




15.87 




21.16 




1 


7.74 




2 


15.49 


16. 




15.62 




20.83 




1 


7.25 




2 


14.5 


16.5 




15.15 




20.2 




1 


6.3 




2 


12.6 


17. 




14.7 




19.6 




1 


5.41 




2 


10.82 


17.5 




14.28 




19.05 




1 


4.57 




2 


9.14 


18. 




13.88 




18.51 




1 


3.77 




2 


7.55 


18.5 




13.51 




18.01 




1 


3.02 




2 


6.05 



EXAMPLES. 189 

If 30 yards of roving, with a 24 teeth change-wheel, weigh 2 
dwts., 14 J grains; what number of grains will the same length 
weigh with a 22 teeth change-wheel (driving) ? 
2 dwts., 14J grs., = 62.5 grs., weight of 30 yds. with 24 tth. whl. 
22 teeth change-wheel. 



1250 
1250 



Chn. whl. 24 tth.)137 5.0(57.29, or 2 dwts., 9J grains. 
120 



175 

168 



70 
48 

220 
216 



If 62J grains of roving require a 24 teeth change-wheel, or 
pinion; what change- wheel, or pinion will there be required to 
produce a hank-roving the same length which will weigh 57 J 
grains? 



57.25 grains, weight required. 

24 teeth, change-pinion, or wheel. 



22900 
11450 



Given weight, 62.5 grs.)1374.00(22 teeth, nearly, change-wheel, 
1250 or pinion required. 

1240 

1250 — nearly. 

iV. B. — When the number of grains which any given length 
weighs, is taken instead of the hank, multiply the grains by 
the change-wheel, or pinion you intend putting on, and divide 
by the change-wheel you have working, and the quotient will be 
the weight in grains required. 



190 EXAMPLES. 

The following will be the dividends for any number of leas, 
from 1 to 7 leas, or 1 hank : — 

iV. B. — For as many leas that you weigh, take as many thousands 
for your dividend, as shown in the annexed table of dividends. 

Leas. Dividends. 

1 1000 

2 2000 

3 3000 

4 4000 

5 5000 

6 6000 

7 7000 

What will 2 leas of 22 \ hank-roving, or yarn weigh ? 

Hank-roving, or yarn, 22.5)2000.0(88.888 grs, or 3 dwts. 16.88 

1800 grains. 

2000 
1800 



2000 

1800 



2000 

1800 

2000 

1800 

200 

If 2 leas weigh 3 dwts., 17 grains; what hank will it be? 

3 dwts., 17 grains = 89 grs.)2000(22.5, or 22J hanks, nearly. 

178 



220 
178 



420 

445 — nearly. 



ROVING AND YARN-TABLE. 



191 



ROVING AND YARN-TABLE. 

From 19 to 33.5 banks for 1, 2, 3, and 4 leas. 



Hank 
roving. 


i 


lea. 


2 leas. 


3 leas. 


4 leas. 


dvvts. 


grains. 


oz.j dwts. 


grains. 


dwts. 


grains. 


oz 


dwts. 


grains. 


19. 


2 


4.63 




4 


9.26 


6 


13.89 




8 


18.52 


19.5 


2 


2.28 




4 


6.56 


6 


9.84 




8 


13.12 


20. 


2 


2. 




4 


4. 


6 


6. 




8 


8. 


20.5 


2 


0.78 




4 


1.56 


6 


2.34 




8 


3.12 


21. 


1 


23.61 




3 


23.23 


I 


22.85 




7 


22.47 


21.5 


1 


22.51 




3 


21.02 


19.53 




7 


18.40 


22. 


1 


21.45 




3 


18.9 


5 


16.36 




7 


13.81 


22.5 


1 


20.44 




3 


16.88 


5 


13.33 




7 


9.77 


23. 


1 


19.47 




3 


14.95 


5 


10.43 




7 


5.61 


23.5 


1 


18.55 




3 


13.1 


5 


7.65 




7 


2.2 


24. 


1 


17.66 




3 


11.33 


5 


5. 




6 


22.6 


24.5 


1 


16.81 




3 


9.63 


5 


2.44 




6 


19.26 


25. 


1 


16. 




3 


8. 


5 


0. 




6 


16. 


25.5 


1 


15.21 




3 


6.43 


4 


21.64 




6 


12.86 


26. 


1 


14.46 




3 


4.92 


4 


19.38 




6 


9.84 


26.5 


1 


13.73 




3 


3.47 


4 


17.2 




6 


6.94 


27. 


1 


13.03 




3 


2.07 


4 


15.11 




6 


4.14 


27.5 


1 


12.36 




3 


0.72 


4 


13.09 




6 


1.44 


28. 


1 


11.71 




2 


23.42 


4 


11.14 




5 


22.85 


28.5 


1 


11.08 




2 


22.17 


4 


9.26 




5 


20.34 


29. 


1 


10.48 




2 


20.96 


4 


7.44 




5 


17.93 


29.5 


1 


9.89 




2 


19.79 


4 


5.69 




5 


15.58 


30. 


1 


9.33 




2 


18.66 


4 


4. 




5 


13.33 


30.5 


1 


8.78 




2 


17.57 


4 


2.36 




5 


11.14 


31. 


1 


8.25 




2 


16.51 


4 


0.76 




5 


9.03 


31.5 


1 


7.74 




2 


15.39 


3 


23.23 




5 


6.78 


32. 


1 


7.22 




2 


14.5 


3 


21.75 




5 


5. 


32.5 


1 


6.76 




2 


13.53 


3 


20.3 




5 


3.16 


33. 


1 


6.3 




2 


12.6 


3 


18.9 




5 


1.21 


33.5 


1 


5.85 




2 


11.7 


3 


17.55 


4 


23.4 



For Yarn-Tables from No. 1 to 300, and from 1 to 7 leas, and 
10 hanks in length, see Tables published by Robert Scott. 



192 SELF-ACTING MULES. 



SELF-ACTING MULES. 

The speed of the twist-shaft is required from the following 
particulars : — 

Revolutions of lying-shaft a minute, 136. 
Diameter of drum on shaft, 21 inches. 
Diameter of pulley on counter-shaft, 14 inches. 
Diameter of drum on counter-shaft, 16 inches. 
Diameter of pulleys on twist-shaft, 12 inches. 

136 revolutions of lying-shaft a minute. 
21 inches, diameter of drum on lying-shaft. 

136 

272 



2856 

16 inches, diam.'of drum on counter-shaft. 



17136 

2856 



45696 dividend. 

14 inches, diam. of pulley on counter-shaft* 
12 inches, diam. of pulleys on twist-shaft. 



168 divisor. 

168)45696(272 revolutions of twist-shaft a min. 
336 



1209 
1176 



336 
336 

iV. B. — The self-acting mules from which these calculations are 
made, are spinning numbers 36 's pin cops for power loom 
weaving. 

The speed of the spindles is required from the following par- 
ticulars : — 



SELF-ACTING MULES. 193 

Revolutions of twist-shaft a minute, 272. 

Diameter of grooved pulley on twist-shaft, 17f inches. 

Diameter of grooved twist-pulley for driving vertical shaft, 10J- 

inches. 
Diameter of grooved pulley on vertical shaft, 10 J inches. 
Diameter of grooved pulley on tin drums, 10 inches. 
Diameter of tin drums, driving spindles, 10 inches. 
Diameter of spindle-wharves, j inch. 

jV. B. — There are generally 3 grooves in the band-pulley on the 
twist-shaft, the diameters of which are 17 f, 18, and 18f inches. 

When the driving and driven-pulleys, or drums, are alternately 
of the same dimensions as in the above question, they are omitted 
in the work. 

272 revolutions of twist-shaft a minute. 
17.375, or 17f inches, diameter of groove in 

pulley on twist-shaft. 

1360 
1904 
816 
1904 
272 



4726.000 dividend. 

The divisor will be .875, which is equal to 7-8ths of an inch, 
the diameter of the spindle-wharves. 

.875)4726.000(5401.1428 revolutions of spindles 
4375 a minute. 



3510 
3500 




1000 
875 


2500 
1750 


1250 

875 


7500 
7000 

Rftft 


3750 

3500 



194 SELF-ACTING MULES. 

The speed of the vertical shaft is required from the following 
particulars: — 

Revolutions of twist-shaft a minute, 272. 
Diameter of groove in pulley on twist-shaft, 17f inches. 
Diameter of grooved twist-pulley for driving vertical-shaft, 10J 
inches. 

272 revolutions of twist-shaft a minute. 
17.375, or 17f inches, diameter of groove in 

pulley on twist-shaft. 

1360 
1904 
816 
1904 
272 



4726.000 dividend. 

The divisor will be 10.25, or 10} inches, the diameter of the 
grooved twist-pulley for driving vertical shaft. 

10.25)4726.00(461.07317 revolutions of vertical shaft 
4100 a minute. 

6260 
6150 

1100 
1025 

7500 
7175 

3250 

3075 

1750 
1025 

7250 
7175 

75 



SELF-ACTING MULES. 195 

W. B. — There is a 40 teeth-wheel on the grooved tioist-pulley- 
shaft, which works into a 40 teeth-wheel on the foot of the ver- 
tical-shaft; but one being a driving and the other a driven- 
wheel, and each containing the same number of teeth, they are 
omitted in the above question and example. 

The speed of the front rollers is required from the following 
particulars : — 

Revolutions of twist-shaft a minute, 272. 

Back pinion on twist-shaft, 18 teeth. 

Back intermediate wheel, 42 teeth. 

Back adjustable intermediate wheel, 70 teeth. 

Back change-wheel on back-shaft, 50 teeth. 

Wheel on back-shaft driving front rollers, 40 teeth. 

Wheel on front rollers, connected with catch-box, 40 tth. 

272 revolutions of twist-shaft a minute. 
18 teeth, back pinion on twist-shaft. 

2176 

272 

4896 dividend. 

The divisor will be 50, being the number of teeth in the change- 
wheel on the back-shaft. All the other wheels, with the exception 
of the back pinion on the twist-shaft, are omitted, on account of 
being connecting, or driving and driven-wheels containing the 
same number of teeth. 

5.0)489.6 



97.92 revols. of front rollers a minute. 

If the front rollers at the mules be 1 inch diameter, making 
97.92 revolutions a minute; how many inches will they traverse ? 
3.1416 circumference when the diameter is 1. 
97.92 revolutions of front rollers a minute. 



62832 
282744 
219912 

282744 

307.625472 inches, front rollers traverse a minute. 



196 SELF-ACTING MULES. 

The speed of the middle rollers is required from the following 
particulars : — 

Revolutions of front rollers a minute, 97.92. 
Wheel on the front rollers, 20 teeth. 
Crown-wheel, 108 teeth. 
Change-pinion, 24 teeth. 
Wheel on the back rollers, 50 teeth. 
Wheel on the end of back rollers, working into stud-wheel which 

drives middle rollers, 32 teeth. 
Wheel on the middle rollers, 25 teeth. 

97.92 revolutions of front rollers a minute. 
20 teeth, wheel front rollers. 



1958.40 

24 teeth, change-pinion, 



78336 
39168 



47001.6 

32 teeth, wheel on the end of back rollers. 



940032 
1410048 



1504051.2 dividend. 



108 teeth, crown-wheel. 

50 teeth, wheel on the back rollers. 



5400 

25 teeth, wheel on the middle rollers. 



27000 
10800 



135000 divisor. 
r 5)1504.051.2 



135.000 thus 



5x9x3=13^ 9)300.81024 
L 3)33.42336 



11.14112 revolutions of middle rollers a 
minute. 



SELF-ACTING MULES. 197 

If the middle rollers be f- of an inch diameter, making 11.14112 
revolutions a minute; how many inches will they traverse ? 

11.14112 revolutions of middle rollers a min. 
.75 or f inch diameter of middle rollers. 



5570560 

7798784 



8.3558400 
3.1416 circumference when the diameter is 1. 



5013504 

835584 
3342336 

835584 
2506752 



26.250706944, or rather more than 26J- inches, mid- 
dle rollers traverse a minute. 
The speed of the back rollers is required from the following 
particulars: — 

Revolutions of the front rollers a minute, 97.92. 

Wheel on the front rollers, 20 teeth. 

Crown-wheel, 108 teeth. 

Change-pinion, 24 teeth. 

Wheel on the back rollers, 50 teeth. 

97.92 revolutions of front rollers a minute. 
20 teeth, wheel on front rollers. 



1958.40 

24 teeth, change-pinion. 



78336 
39168 



47001.6 dividend. 
108 teeth, crown wheel. 

50 teeth, wheel on the back rollers. 



*a tu\ a- • f 9)470.01.6 
54.00 divisor, or J J_ 

9 x 6 = 54 | 6)52.224 



8.704 revolutions of back rol- 
lers a minute. 



198 SELF-ACTING MULES. 

If the back rollers be -Jths of an inch diameter, making 8.704 
revolutions a minute ; how many inches will they traverse ? 

8.704 revolutions of back rollers a minute. 
.875, or {ths of an inch, diam. of rollers. 



43520 

60928 
69632 



7.616000 
3.1416 circumference when the diameter is 1. 



45696 

7616 
30464 
7616 

22848 

23.9264256, or nearly 24 inches, back rollers traverse 
a minute. 

The draught between the middle and back rollers is required 
from the following particulars : — 

Middle rollers traverse 26.250706944 inches a minute. 
Back rollers traverse 23.9264256 inches a minute. 
23.9264256)26.250706944(1.0971428, or nearly 1 T ^ draught 
239264256 between the mid. and 



2324281344 
2153378304 

1709030400 

1674849792 

341806080 
239264256 

1025418240 
957057024 



back rols. 



2050836480 

683612160 1914114048 

478528512 

- 136722432 



SELF-ACTING MULES. 199 

The draught between the front and middle rollers is required 
from the following particulars : — 

Front rollers traverse 307.625472 inches a minute. 
Middle rollers traverse 26.250706944 inches a minute. 
26.250706944)307.62547200(11.71875 draught between the 
26250706944 front and mid. rollers. 



45118402560 
26250706944 

188676956160 

183754948608 

49220075520 
26250706944 

229693685760 
210005655552 

196880302080 
183754948608 

131253534720 
131253534720 

The draught between the front and back rollers is required 
from the following particulars: — 

Front rollers traverse 307.625472 inches a minute. 
Back rollers traverse 23.9264256 inches a minute. 
23.9264256)307.625472(12.857 draught between the front 
239264256 and back rollers. 



683612160 

478528512 

2050836480 
1914114048 

1367224320 
1196321280 



1709030400 
1674849792 

34180608 



200 SELF-ACTING MULES. 

The draught between the front and back rollers is required 
from the following particulars : — 

Draught between the front and middle rollers, 11.71875. 
Draught between the middle and back rollers, 1.09714. 

11.71875 draught between front and mid. rols. 
1.09714 draught between middle and back rols. 



4687500 
1171875 
8203125 
10546875 
11718750 

12.8571093750 draught between the front and back 

rollers. 

The draught between the front and middle rollers is required 
from the following particulars : — 
Wheel on front rollers, 20 teeth. 
Crown-wheel, 108 teeth. 
Change-pinion, 24 teeth. 
Wheel on back rollers, 50 teeth. 
Wheel on the end of back rollers, working a stud-wheel which 

drives the middle rollers, 32 teeth. 
Wheel on middle rollers, 25 teeth. 
Diameter of front rollers, 1 inch or fths. 
Diameter of middle rollers, f inch, or fths. 

DRIVING-WHEELS. 

20 teeth, wheel on front rollers. 
24 teeth, change-pinion. 



480 
32 teeth, wheel on the end of back rollers. 



960 
1440 



15360 

6 

8 



Hhs, or | inch diameter of middle rollers. 



92160 divisor. 



SELF-ACTING MULES. 201 



DRIVEN-WIIEELS. 



108 teeth, crown wheel. 

50 teeth, wheel on back rollers. 



5400 
.25 teeth, wheel on middle rollers. 



27000 
10800 

135000 

fths, or 1 inch, diameter of front rols. 



1080000 dividend. 

92160)1080000(11.71875 draught between the front and 
92160 middle rollers. 



158400 
92160 

662400 
645120 

172800 
92160 



806400 
737280 

691200 
645120 

460800 
460800 

The draught between the front and back rollers is required 
from the following particulars : — 

Wheel on front rollers, 20 teeth. 
Crown-wheel, 108 teeth. 
Change-pinion, 24 teeth. 
Wheel on back rollers, 50 teeth. 
14 



202 SELF-ACTING MULES. 

Diameter of front rollers, 1 inch, or f ths. 
Diameter of back rollers, J inch, or Jths. 

DRIVING-WHEELS. 

20 teeth, wheel on front rollers. 
24 teeth, change-pinion. 



480 



ths, or | inch, diam. of back rollers. 



. 



3360 divisor. 

DRIVEN-WHEELS. 

108 teeth, crown-wheel. 

50 teeth, wheel on back rollers. 



5400 

| ths, or 1 inch, diameter of front rollers. 



43200 dividend. 



3360)43200(12.8571 draught between the front and 
3360 back rollers. 



9600 
6720 

28800 
26880 

19200 
16800 

24000 
23520 

4800 
3360 

1440 



N. B. — By examining the different systems of working draughts 
as shown in the last examples, it will be found that they all 
agree with each other ; therefore, any of the systems may be 
adopted. 



SELF-ACTING MULES. 203 

The speed of the long drawing-out shaft is required from the 
following particulars : — 

Revolutions of twist-shaft a minute, 272. 
Back pinion on twist-shaft, 18 teeth. 
^ J Back intermediate wheel, 42 teeth. 
\ Back adjustable intermediate wheel, 70 teeth. 
Back change-wheel on back shaft driving front rols. 50 teeth. 
Wheel on back shaft, 19 teeth. 
Back change-wheel on long drawing-out shaft, 61 teeth. 

272 revolutions of twist-shaft a minute. 
18 teeth, back pinion on twist-shaft. 



2176 

272 



4896 

19 teeth, wheel on back shaft. 



44064 

4896 



93024 dividend. 

50 teeth, change-wheel on back shaft, for driving front rols. 
61 teeth, back change-wheel on long drawing-out shaft. 



3050 divisor. 



3050)93024(30.499, or nearly 30J revolutions of long 
9150 drawing-out shaft a min. 



15240 
12200 

30400 
27450 

29500 
27450 

2050 

* These are only carrying or connecting-wheels; consequently, they are omitted 
the work. 






204 SELF-ACTING MULES. 

The speed of the drawing-out scroll-shaft is required from the 
following particulars: — 

Revolutions of long drawing-out shaft a minute, 30.5. 
Bevil-wheel on long drawing-out shaft, 24 teeth. 
Bevil-wheel on scroll-shaft, 48 teeth. 

30.5 revols, of long drawing-out shaft a min. 
24 teeth, bevil-wheel on drawing-out shaft. 



1220 
610 



Teeth of bev. ] ■ 

wl. on scroll- > 48)732.0(15.25 revolutions of drawing-out scroll- 
shaft, J 48 shaft a minute. 



252 
240 

120 
96 



240 

240 



The speed of the drawing-out scroll-shaft is required from the 
following particulars:— 

.Revolutions of twist-shaft a minute, 272, 

Back pinion on twist-shaft, 18 teeth. 

Back change-wheel on back shaft, for driving front rollers, 50 

teeth. 
Wheel on back shaft, 19 teeth. 

Back change- wheel on long drawing- out shaft, 61 teeth* 
Bevil-wheel on long drawing-out shaft, 24 teeth. 
Wheel ob drawing-out scroll-shaft^ 48 teeth. 



SELF-ACTING MULES. 205 

272 revolutions of twist-shaft a minute. 
18 teeth, back pinion on twist-shaft. 



2176 

272 



19 teeth, wheel on back shaft. 



44064 

4896 



93024 

24 teeth, bevil- wheel on long drawing-out shaft. 



372096 

186048 



2232576 dividend. 

50 teeth, back change-whl. on back shaft, for driv* front ro!s< 
61 teeth, back change-wheel on long drawing-out shaft. 



3050 

48 teeth, bevil-wheel on drawing-out scroll-shaft. 



24400 
12200 



146400 divisor. 



146400)2232576(15.25, or 15 J revolutions nearly, 
146400 drawing-out scroll a min, 

768576 
732000 



365760 
292800 



729600 
732000— nearly. 



206 SELF-ACTING MULES. 

If the drawing-out scroll be 6} inches diameter, making 15J- 
revolutions a minute ; how many inches will the scroll, or carriage 
traverse? 

15.25, or 15J revolutions of scroll a minute. 
6.75, or 6f inches, diameter of scroll. 



7625 • 
10675 
9150 

102.9375 

3.1416 circumference when the diameter is 1. 



6176250 
1029375 
4117500 
1029375 

3088125 • 



323.38845000, or nearly 323 T % inches, drawing-out 

scroll traverses a minute. 

The length delivered by the front rollers a stretch is required 
from the following particulars : — 

Carriage, or drawing-out scroll traverses 323.38845 inches a 

minute. 
Front rollers traverse 307.625472 inches a minute. 
Length of stretch put up, 60.5, or 60J inches. 

307.625472 inches front rollers traverse a min. 
60.5, or 60J inches length of stretch. 



1538127360 

18457528320 

18611.3410560 dividend. 



SELF-ACTING MULES. 207 

Car. travs. a min. 323.38845 in.)18611. 3410560(57.551 in., front 

161694225 rollers deliver a 
stretch. 



244191855 
226371915 

178199406 
161694225 

165051810 
161694225 

33575850 
32338845 



1237005 



If the length delivered at the front rollers a stretch, be 57.551 
inches, and the length of the stretch put up, be 60.5, or 60J 
inches; how many inches a stretch does the carriage gain? 

60.500, or 60J inches, length of stretch put up. 
57.551 inches, length deliv. at front rols. a stretch. 

2.949, or nearly 3 inches gain of carriage. 

The draught between the carriage and front rollers is required 
from the following particulars: — 

Carriage traverses 323.38845 inches a minute. 
Front rollers traverse 307.625472 inches a minute. 
307.625472)323.388450(1.05124 draught between carriage 
307625472 and front rollers. 



1576297800 
1538127360 

381704400 
307625472 



740789280 
615250944 

1255383360 
1230501888 

24881472 



208 SELF-ACTING MULES. 

The length of the stretch is required from the following par- 
ticulars : — 

Front rollers deliver 57.551 inches a minute. 
Draught between carriage and front rollers, 1.05124. 
57.551 inches, front rollers deliver a minute. 
1.05124 draught between carriage and front rollers. 



230204 
115102 

57551 
287755 
576510 

60.49991324, or 60J inches, length of stretch. 

The total draught at mules is required from the following 
particulars : — 

Draught between front and back rollers, 12.857109375. 
Draught between carriage and front rollers, 1.05124. 

12.857109375 draught between front and back rols. 
1.05124 draught between car. and front rols. 



51428437500 

25714218750 
12857109375 

64285546875 
128571093750 



13.51590765937500, orrather morethan!3| total draught 
at mules. 

The total draught at mules is required from the following par- 
ticulars : — 

Revolutions of drawing-out scroll a minute, 15.25. 
Revolutions of back rollers a minute, 8.704. 
Diameter of scroll, 6f inches, or 54-8ths. 
Diameter of back rollers, J inches, or 7-8ths. 

15.25 revolutions of drawing-out scroll a min. 
54-8ths, or 6f inches, diameter of drawing- 

■ out scroll. 

6100 
7625 



823.50 dividend. 



SELF-ACTING MULES. 209 

8.704 revolutions of back rollers a minute. 
7-8ths, or | inch, diameter of back rollers. 



60.928 divisor. 

Divisor. Dividend. 

60.228)823.500(13.515 total draught at mules. 
60928 



214220 

182784 

314360 
304640 



97200 
60928 

362720 
304640 

58080 

The total draught at mules is required from the following par- 
ticulars : — 

Bevil-wheel on drawing-out scroll-shaft, 48 teeth. 
*Bevil-wheel on long drawing-out shaft, 24 teeth. 

Back change-w T heel on drawing-out shaft, 61 teeth. 

Wheel on back shaft, 19 teeth. 

Wheel on front rollers, 20 teeth. 

Crown-wheel, 108 teeth. 
*Change-pinion, 24 teeth. 

Wheel on back rollers, 50 teeth. 

Diameter of drawing-out scroll, 6} inches, or 54-8ths. 

Diameter of back rollers, J inch, or 7-8ths. 

* These wheels are omitted in working, one being a driving and the other a 
driven-wheel, each containing the same number of teeth. 



210 SELF-ACTING MULES. 



DRIVING-WHEELS. 

48 teeth, bevil-wheel on drawing-out scroll-shaft. 
61 teeth back change-wheel on drawing-out shaft. 



48 

288 



2928 



20 teeth, wheel on front rollers. 



58560 

7-8ths inch, diameter of back rollers. 



409920 divisor. 

DRIVEN-WHEELS. 

19 teeth, wheel on back shaft. 
108 teeth, crown-wheel. 

152 

190 



2052 

50 teeth, wheel on back rollers. 



102600 

54-8ths, or 6| in. diam. of drawing-out scroll. 



410400 

513000 



5540400 dividend. 

409920)5540400(13.5158 total draught at mules. 
409920 



1441200 
1229760 


2380800 


2114400 

2049600 


2049600 


3312000 


648000 
409920 


3279360 




S9fU0 



SELF-ACTING MULES. 211 

^V. B. — By changing the 50 teeth wheel on the bach shaft, it will 
affect the front rollers and drawing -out scroll in the same 
p>roportion; consequently, the gain, or draught at carriage, will 
remain the same. The gain, or draught at carriage, may be 
altered by changing the 61 teeth wheel on the long drawing- 
out shaft; both being driv en-wheels from the first moving power, 
a less number of teeth will increase the speed, whereas, had 
they been driving -ivheels, it would have required a greater 
number of teeth to have produced an increase of speed, and the 
reverse for a decrease in 



The speed of the quadrant-shaft is required from the following 
particulars: — 

Revolutions of drawing-out scroll a minute, 15.25. 

Diameter of scroll, 6.75 inches. 

Diameter of drum on quadrant- shaft, 6.125. 

15.25 revols. of drawing-out scroll a minute. 
6.75, or 6| inches, diameter of scroll. 



7625 
10675 
9150 

102.9375 

Diam. of drum on quad.-shaft, 6.125 in.)102.9375(16.806 revols. 

6125 of quad.-shaft 



41687 
36750 

49375 

49000 



a mm. 



37500 
36750 

750 



N". B. — The quadrant- shaft is driven by the drawing-out scroll 
band while the carriage is drawing out, and the chain on the 
winding-on drum is counterbalanced by a weight at the end of 
a band working on pulleys and connected with the winding-on 



212 SELF-ACTING MULES. 

drum, lohich is out of geer while drawing out, and is put into 
geer by a spring connected with the long lever and vertical 
shaft when the carriage is going in; during which time, the 
speed of the winding-on drum is governed by a strap working 
the governor -wheels connected with the worm, when the slide 
to which the winding-on chain is affixed rises in the recess of 
the quadrant by means of the worm, and decreases the length 
of the chain from the drum, regulating the winding on accord- 
ing to the increasing thickness of the cop. When the cop has 
attained the intended thickness, then the g over nor -icheels cease 
to ivork, and the length of the chain going on the winding-on 
drum remains the same till the cop is completed. 

The number of teeth the quadrant moves a stretch is required 
from the following particulars : — 

Carriage traverses 323.38845 inches a minute. 
Revolutions of quadrant-shaft a minute, 16.806. 
Wheel on quadrant-shaft, 22 teeth. 
Length of stretch, 60J- inches. 

16.806 revols. of quad. -shaft a min. 
22 teeth, wheel on quad.-shaft. 



33612 
33612 



369.732 

60.5, or 60J in., length of stretch. 



1848660 
22183920 
Car. travs., 323.38845 in.)22368.7860(69.1T num. of teeth quad. 

194033070 moves a stretch of 

60J inches. 



296547900 
291049605 

54982950 
32338845 

226441050 
226371915 



69135 



SELF-ACTING MULES. 213 

The turns an inch of yarn are required from the following 
particulars : — 

Bell-wheel worked by a worm on the twist-shaft, 56 teeth. 
Diameter of the grooved pulley on the twist-shaft, 17f inches. 
Diameter of grooved twist-pulley, driving vertical shaft, 10J 

inches. 
Diameter of grooved pulley on the vertical shaft, 10J inches. 
Diameter of grooved pulley on tin drums, 10 inches. 
.Diameter of tin drums, driving the spindles, 10 inches. 
Diameter of wharves on the spindles, J inch. 
Length of stretch put up, 60J inches. 

17.375, or 17f inches, diam. of grooved pul. on 
56 teeth, bell-wheel. [the twist-shaft. 

104250 

86875 



973.000 dividend. 

.875, or |ths of an inch, diam. of wharves. 
60.5, or 60J inches, length of stretch. 



4375 

52500 

52.9375 divisor. 

52.9375)973.0000(18.38 turns an inch of yarn 
529375 required. 

4436250 
4235000 



2012500 
1588125 

4243750 
4235000 



8750 

* These are all omitted in the work, being driving and driven, of the same 
dimensions. 



214 SELF-ACTING MULES. 

The number of teeth in the bell-wheel is required from the 
following particulars : — 

Number of turns an inch of yarn required, 18.38. 
Length of stretch put up, 60.5 inches. 
Diameter of wharves on the spindles, -g- inch. 
f Diameter of drum driving wharves, 10 inches, 
jjj ! Diameter of pulley on drum driving wharves, 10 inches. \ 
» Diameter of pulley on vertical shaft, 10J- inches. 
Diameter of pulley driving vertical shaft, 10J inches. 
Diameter of pulley on twist-shaft, 17f inches. 

18.38 turns an inch. 
60.5 inches, length of stretch. 



U 



9190 
110280 

1111.990, or 1112 turns in a st'ch of 60J in. 
.875, or | inch, diam. of spindle wharves. 



555995 
778393 
889592 

In. diam. *} 

of pul. on V 17.375)972.99125(56 nearly, number of teeth re- 
twist-s'ft, j 86875 quired in the bell-wheel. 

104241 
104250— nearly. 

JST. B. — All the rules are fully laid down in a former part of 
this work. (See Hand Mules.) 

The speed of the short going-in shaft is required from the fol- 
lowing particulars : — 

Revolutions of twist-shaft a minute, 272. 
Wheel on loose pulley, 36 teeth. 
Wheel on short going-in shaft, 54 teeth. 

* These are omitted in the work on account of being driving and driven of the 
same dimensions; but if the diameters had been of different dimensions, they must 
have been made use of as in former examples. 



SELF-ACTING MULES. 215 

272 revolutions of twist-shaft a minute. 
36 teeth, wheel on loose pulley. 



1632 

816 

Teeth of wheeH 

on short going-in V 54)9792(181.33, or 181J revolutions of short 
shaft, J 54 going-in shaft a minute. 



439 
432 



72 
54 

180 
162 

180 
162 

18 

The speed of the long going-in shaft is required from the 
following particulars: — 

Revolutions of twist-shaft a minute, 272. 
Wheel on loose pulley, 36 teeth. 
Wheel on short going-in shaft, 54 teeth. 
Wheel on short going-in shaft, 17 teeth. 
Wheel on long going-in shaft, 20 teeth. 

272 revolutions of twist-shaft a minute. 
36 teeth, wheel on loose pulley. 



1.632 
816 



9792 

17 teeth, wheel on short going-in shaft. 



68544 

9792 



166464 dividend. 



216 SELF-ACTING MULES. 



54 teeth, wheel on short going-in shaft. 
20 teeth, wheel on long going-in shaft. 



1080 divisor. 

1080)166464(154.133 revolutions of long going-in 
1080 shaft a minute. 



5846 
5400 

4464 
4320 



1440 

1080 



3600 
3240 

3600 
3240 

360 

The speed of the going-in scroll-shaft is required from the 
following particulars : — 

Revolutions of twist-shaft a minute, 272. 
Wheel on loose pulley, 36 teeth. 
Wheel on short going-in shaft, 54 teeth. 
Wheel on short going-in shaft, 17 teeth. 
Wheel on long going-in shaft, 20 teeth. 
Bevil- wheel on long going-in shaft, 16 teeth. 
Bevil-wheel on scroll-shaft, 45 teeth. 

272 revolutions of twist-shaft a minute. 
36 teeth, wheel on loose pulley. 

1632 
816 

9792 



SELF-ACTING MULES. 217 

9792 
17 teeth, wheel on short going-in shaft. 



68544 
9792 



166464 

16 teeth, bevil- wheel on long going-in shaft. 



998784 
166464 



2663424 dividend. 



54 teeth, wheel on short going-in shaft. 
20 teeth, wheel on long going-in shaft. 



1080 
45 teeth, bevil- wheel on scroll-shaft. 



5400 
4320 



48600 divisor. 

48600)2663424(54.80296 revolutions of going-in 
243000 scroll a minute. 



230424 
194400 

390240 

388800 



144000 
97200 

468000 
437400 

306000 
291600 

14400 
15 



218 SELF-ACTING MULES. 

The revolutions of the going-in scroll a stretch, are required 
from the following particulars: — 

Circumference, or chase of scroll a stretch, 22 inches. 
Length of stretch put up, 60J inches. 

22)60.5(2.75, or 2f revolutions of going-in 
44 scroll a stretch. 



165 
154 

110 
110 



The speed of the backing-off wheel is required from the fol- 
lowing particulars: — 

Revolutions of long going-in shaft a minute, 154.133. 
Wheel on long going-in shaft, 12 teeth. 
Backing-off wheel, 77 teeth. 

154.133 revols. of long going-in shaft a min. 
12 teeth, wheel on long going-in shaft. 



Teethofback-| 77)1849>600(24>02 reyolg> f backing-off wheel 
mg-offwheel,J L \ ^ . . * 



154 a minute 

309 

308 



160 
154 

6 

N. B. — The haching-off wheel can be regulated by the leather fric- 
tion pulley, which works into the backing-off wheel, and may 
be made slacker, or tighter, by means of a bolt and nut con- 
nected with the friction pulley. The proper friction on the 
backing-off wheel is very essential, which will soon be ascer- 
tained by any practical person. 

Required, from the following particulars, the length of time a 
stretch the carriage occupies while going in. 



SELF-ACTING MULES. 



219 



Revolutions of going-in scroll a minute, 54.80296. 
Revolutions of going-in scroll a stretch, 2.75. 

2.75 revols. of going-in scroll a 
60 seconds, 1 min. [stretch. 



Revols. of going-in j 5 4<80 296)165.00000(3.010786 
scroll a minute, j i«^n«8ft 



.6440888 

5911200 
5480296 

43090400 

38362072 

47283280 
43842368 

34409120 

32881776 



or rather 
more than 
3 seconds 
a stretch. 



1527344 



If it requires 56 turns or revolutions of the twist-shaft to draw 
out one stretch, what time will it require, if the twist-shaft makes 
272 turns or revolutions a minute ? 

272)56.0(.20588 minute a stretch. 
544 



1600 
1360 

2400 
2176 

2240 
2176 



64 

,20588 minute a stretch. 
60 seconds, 1 minute. 



12.35280 seconds required to draw out 1 

stretch. 



220 SELF-ACTING MULES. 

The number of stretches a mule a minute is required from 
the following particulars, allowing 2J seconds a stretch for 
backing off. 

Drawing out a stretch, 12.3528 seconds. 
Backing off a stretch, 2.5 seconds. 
Going in a stretch, 3.0107 seconds. 



17.8635 seconds a stretch. 

17.8635)60.0000(3.3588, or rather more than 3^ stretches 
535905 a minute, each mule. 



640950 
535905 

1050450 

893175 

1572750 
1429080 

1436700 

1429080 

7620 

If a mule produce 3.3588 stretches a minute, and each stretch 
be 60 inches, how many hanks a spindle will be produced in one 
week, allowing them to work successively for 65 hours ? 

3.3588 stretches a minute. 
60 minutes, 1 hour. 



201.5280 stretches an hour. 
65 hours in 1 week. 



1007640 

1209168 



13099.320 stretches in 1 week, 
60 inches each stretch. 



785959.200 inches of yarn a spindle a week. 






SELF-ACTING MULES. 221 



- 1 • ) 6)785959.2 inches of yarn a spindle a week. 
36 inches > J 6)130993.2 

21832.2 yards a spindle a week. 



1 hank is 840 yds.)21832.2(25.99 nearly 26 hanks a spindle a 
1680 " week. 



5032 
4200 

8322 
7560 



7620 
7560 



60 

The speed of the leather-contact pulley is required from the 
following particulars : — 

Revolutions of twist-shaft a minute, 272. 

Wheel on loose pulley, 36 teeth. 

Wheel on leather-contact pulley shaft, 33 teeth. 

272 revolutions of twist-pulley a min. 
36 teeth, wheel on loose pulley. 



1632 

816 

Teeth-wheel on "} 

leather-contact V 33)9792(296.727 revols. of leather-contact 
pulley, J 66 pulley a minute. 

319 

297 

222 90 

198 66 

240 240 

231 231 

90 9 



222 SELF-ACTING MULES. 

If the leather-contact pulley be 3f inches diameter, making 
296. 727 revolutions a minute, what will it traverse ? 

296.727 revols. of leather-contact pulley a min. 
8.75, or 3f inches, diameter of do. 



1483635 
2077089 
890181 



1112.72625 

3.1416 circumference when the diameter is 1. 



667635750 
111272625 
445090500 
111272625 

333817875 



3495.740787000 inches leather-contact pulley traverses 

a minute. 

The revolutions of the spindles for the twist-shaft once are re- 
quired from the following particulars : — 

Revolutions of spindles a stretch, 1112. 
Revolutions of twist-shaft a stretch, 56, 

Revols. of twist-shaft 1 8)1112 revols. of spindles a stretch. 

a stretch, is b6 y then V 

8 x 7=56, J 7)139 



19.857 revols. of the spindles for the 
twist-shaft once. 

Required, from the following particulars, the revolutions a 
stretch of the spindles for winding on yarn at the beginning of 
the set — i. e., when the spindles are bare : — 

Diameter of winding-on drum, 4J- or 4.125 inches. 
Length of chain thrown off drum, 60J or 60.5 inches. 
Wheel on the winding-on drum, 41 teeth. 
Pinion on winding-on drum-shaft, 25 teeth. 



SELF-ACTING MULES. 223 

f Bevil-wheel on winding-on drum-shaft, 40 teeth. 
\ Bevil-wheel on foot of vertical shaft, 40 teeth. 
Diameter of pulley on vertical shaft, 10J or 10.25 inches. 
Diameter of spindle-wharves, | or .875 inch. 

4.125 inches, diameter of winding-on drum. 
3.1416 inches, circum. when the diam. is 1. 



24750 

4125 
16500 
4125 
12375 

12.9591000 . . 

25 teeth, pinion on winding-on drum-shaft. 



647955 
259182 



323.9775 

.875 inches, diameter of wharves. 



16198875 
22678425 
25918200 



283.4803125 divisor. 

60.5 in., length of chn. thrown off wind.-on drum. 
41 teeth, wheel on winding-on drum. 

605 
2420 



2480.5 
10.25 inches diam. of pulley on vertical shaft. 



124025 
49610 

248050 

25425.1250000 

* These are omitted in the work, being driving and driven; and the tin drums 
for driving spindles are omitted, being intermediate. 



224 SELF-ACTING- MULES. 

283;4803125)25425.1250000(89.689 revols. of spindle a stretch, 
22678425000 winding yarn on bare spin- 
■ dies. 

27467000000 

25513228125 

19537718750 

17008818750 

25289000000 

22678425000 

26105750000 
25513228125 

592521875 

If it requires the bare or empty spindles to make 89.689 re- 
volutions to wind on a stretch 60 \ inches long; what will the 
circumference and diameter of the spindles be? 

89.689)60.5000(.67455 inch, circumference of spindles. 
538134 



668660 

627823 



408370 
358756 

496140 
448445 

476950 
448445 

28505 



SELF-ACTING MULES. 225 

3.1416).67455(.2147 inch, diameter of spindles. 

62832 



46230 
31416 

148140 
125664 

224760 
219912 

4848 

The speed of the spindles for winding on the yarn will be in 
accordance with their diameter, from which may be ascertained 
the size of the winding-on drum, or pinion on the winding-on 
drum-shaft. 

If the diameter of the spindles be \ inch; how many revolu- 
tions must they make to wind on 60 J inches of yarn? 

3.1416 circumference when the diameter is 1. 
.25, or J inch, diameter of spindles. 



157080 

62832 



.785400 circumference of spindle. 

.7854)60.5000(77 revolutions required for spin- 
54978 die, to wind on 60} inches of 
yarn. 

55220 

54978 



242 

Required, the revolutions of the winding-on drum, for the 
spindles to make 77 revolutions, or turns a stretch, according to 
the following particulars : — 

Diameter of spindle wharves, -J, or .875 inch. 
Diameter of pulley on vertical shaft, 10| inches. 



226 SELF-ACTING MULES. 

Pinion on winding-on drum-shaft, 25 teeth. 
Wheel on winding-on drum, 41 teeth. 

.875 diameter of spindle-wharves. 
77 revols., or turns of spindles a stretch. 



6125 
6125 



67.375 

25 teeth, pinion on winding-on drum-shaft. 



336875 
134750 



1684.375 dividend. 

10.25 inches, diameter of pulley on vertical shaft. 
41 teeth, wheel on winding-on drum. 

1025 
4100 



420.25 divisor. 

420.25)1684.375(4 revolutions of winding-on drum 
168100 a stretch required. 

337 

If the winding-on drum be required to make 4 revolutions a 
stretch; what must the circumference be to wind on 60 J inches 
of chain? 

4)60.5 



15.125, or 15J- inches, circumference of drum. 

If the winding-on drum be 15.125, or 15J inches circumfer- 
ence; what will the diameter be? 



SELF-ACTING MULES. 227 

3.1416)15.1250(4.8144 inches, diameter of winding- 
125664 on drum. 



255860 
251328 



45320 
31416 

139040 
125664 

133760 
125664 

8096 

The iron-contact pulley on the cam-shaft is 5{| inches diame- 
ter, and has 4 recesses, or spaces in it at an equal distance, which 
relieve it from the leather-contact pulley, and is also assisted by 
4 pins in the front of the escape-plate, each of which works 
against a spring, when the spring at the back of the escape-plate 
moves from one bolster to another when acted upon by the lever 
connected, and which gives power, by the assistance of the leather- 
contact pulley, to the different motions on the cam-shaft, which is 
as follows : — 

Motions from the escape-plate. 

First — Back and front cams for the strap-lever. 

Second — Backing-off cam connected with the friction-pulley, 

working into backing-off wheel-pulley. 
Third — Front roller eccentric. 

Fourth — Stop-finger connected with the bell-wheel-shaft. 
Fifth — Going-in eccentric. 
Sixth — Drawing-out eccentric. 

The following are the alternate movements on the cam-shaft 
each stretch : — 

First — Roller geer and drawing-out motions. 
Second — Twist motion. 
Third — Backing-off motion. 
Fourth — Going-in motion. 



228 SELF-ACTING MULES. 



THE FOLLOWING ARE THE PARTICULARS OF THE SELF-ACTING 
MULES : — 

Revolutions of twist-shaft a minute, 272. 
Revolutions of spindles a minute, 5401.1428. 
Revolutions of vertical shaft a minute, 461.07317. 
Revolutions of front rollers a minute, 97.92. 
Revolutions of middle rollers a minute, 11.14112. 
Revolutions of back rollers a minute, 8.704. 
Revolutions of long drawing-out shaft a minute, 30.499 or 30J. 
Revolutions of drawing-out scroll a minute, 15.249 or 15J. 
Revolutions of quadrant-shaft a minute, 16.806. 
Revolutions of short going-in shaft a minute, 181.333. 
Revolutions of long going-in shaft a minute, 154.1333. 
Revolutions of going-in scroll a minute, 54.80296. 
Revolutions of going-in scroll a stretch, 2.75 or 2f . 
Revolutions of backing-off wheel a minute, 24.02. 
Revolutions of leather-contact pulley a minute, 296.727. 
Revolutions of spindles per twist-shaft once, 19.857. 
Revolutions of bare or empty spindles for winding on yarn a 

stretch, at the beginning of set, 89.689. 
Diameter of pulleys on twist-shaft, 12 inches. 
Diameter of grooved band-pulley on twist-shaft, 17f , 8, and 

18| inches. 
Diameter of grooved twist-pulley for driving vertical shaft, 10J 

inches. 
Diameter of grooved pulley on vertical shaft, 10J- inches. 
Diameter of grooved pulley on tin drums, 10 inches. 
Diameter of tin drums for driving spindles, 10 inches. 
Diameter of spindle-wharves, -J inch. 
Diameter of front rollers, 1 inch. 
Diameter of middle rollers, f inch. 
Diameter of back rollers, -J inch. 
Diameter of drawing-out scroll, 6f inches. 
Diameter of quadrant-shaft drum, 6J- inches. 
Diameter of leather-contact pulley, 3f inches. 
Diameter of iron-contact pulley, 5{| inches. 
Diameter of winding-on drum, 4J- inches. 
Diameter of spindles, .2147 inch. 
Front rollers traverse a minute, 307.625472 inches. 
Middle rollers traverse a minute, 26.250707 inches. 
Back rollers traverse a minute, 23.926425 inches. 
Drawing-out scroll traverses a minute, 323.38845 inches. 



SELF-ACTING MULES. 229 

Front rollers traverse a stretch, 57.551 inches. 
Carriage traverses a stretch, 60.5 inches. 
Going-in scroll traverses a revolution, 22 inches. 
Leather-contact pulley traverses a minute, 3495.749787 inches. 
Draught between the middle and back rollers, 1.0971428, nearly 

Draught between the front and middle rollers, 11.71875. 

Draught between the front and back rollers, 12.8571. 

Draught between the front rollers and carriage, 1.05124. 

Total draught at the mules, 13.5158. 

Gain at carriage each stretch, 2.949, nearly 3 inches.. 

Turns each inch in yarn, 18.38. 

Turns each stretch of 60J inches, 1112. 

Bell-wheel, 56 teeth. 

Number of teeth the quadrant moves each stretch of 60J inches, 

69.17. 
Time each stretch drawing carriage out, 12.3528 seconds. 
Time each stretch allowed for backing off, 2.5 seconds. 
Time each stretch carriage going in, 3.0107 seconds. 
Time required to complete each stretch, 17.8635 seconds. 
Number of stretches a minute, each mule, 3.3588. 
Number of stretches an hour, each mule, 201.528. 
Number of stretches a week, each mule, 13099.32. 
Number of hanks a spindle a week, 25.99, or 26 hanks nearly. 

The faller rises by the lowering of the coping-rail, by means 
of a lever connected with the faller-sector working upon it. The 
faller-sector at the same time works into a 22 teeth-wheel on 
the faller-shaft. 

The backing-off eccentric is loose on the vertical shaft; and 
the chain attached to the eccentric and connected with the faller- 
sector is governed by a catch fixed to the plate of the eccentric, 
working against the ratchet-wheel while backing off. 

N". B. — The number of teeth in the ratchet-wheel is 88. 

At the commencement of a set, when the spindles are bare or 
empty, great care must be taken to set the coping-rail and wind- 
ing-on chain to their proper places, by means of the worm or 
screw connected ; for, if right, then they will regulate them- 
selves afterwards. 

Whatever bevil the coping-rail may have will be the length of 
the chase given to the faller, which may be increased or de- 
creased by giving more bevil to the coping-rail, and by changing 
the wheel on the worm-shaft connected with the shaper or coping- 



230 HANK, OR PROPORTION OF HANK, ETC. 

plate. The cop may be made larger or smaller. A larger wheel 
"will make a larger cop, on account of the worm-shaft connected 
with the shaper or coping-plate moving slower ; and a smaller 
wheel will make a smaller cop by the worm-shaft connected with 
the shaper or coping-plate moving quicker, there being a finger 
attached to the carriage which works the catch on the wheel of 
the worm-shaft, and causes the wheel to move one tooth each 
stretch, which gives the bevil to the coping-rail. 

It is of the utmost importance that every attention be given 
to machinery by having every part of the machine properly ad- 
justed, and set square with the scrolls and other bands of a pro- 
per tightness ; and that regular cleaning and oiling be particu- 
larly attended to, which is indispensable in all machinery — the 
neglect of which causes machinery to work ill, and destroys it 
much sooner than it otherwise would have been had proper care 
been taken. 

Neglect always brings the best machinery into disrepute, con- 
sequently is injurious to the best machinists, and trade generally 
suffers materially. 

| | Within these last few years, there have been a number of 
patents obtained by different machinists for improvements in 
machinery, used in all the different operations of carding, draw- 
ing, slabbing, roving, spinning, and weaving. 

HANK, OR PROPORTION OF HANK, ETC. IN EACH OPERATION. 

The following examples will show the hank and the decimal, 
or proportion of hank, in each and every operation, from the 
spinning to the lap machine. 

Suppose the numbers or counts of yarn be 40's, with a draught 
of 9.6, or 9 t 6 q, what hank roving will be required ? 

Draught, 9.6)40.0(4.1666, or 4| hank roving required. 

384 

160 
96 

640 

576 

640 640 

576 576 

640 64 



231 

If the draught at roving-frame be 7.5, or 7J, producing a 4£ 
hank roving, what hank will the slabbing be, allowing 2 slabbings 
to each roving ? 

iV. B. — Where there is doubling, multiply the hank, or propor- 
tion of hank, by the number of ends doubled, and divide by 
the draught. 

Hank roving, 4J, or 4.1666 

2, number of ends doubled. 



Draught 7J, or 7.5)8.3333(1.1111, or lj hank slabbing. 

75 



83 

75 

83 

75 

83 

75 



83 

75 

8 

If the draught at the slabbing-frame be 6.875, and the slab- 
bing be 1.1111, or \\ hank, what decimal or proportion of hank 
will the drawing be, put up at the back of slabbing-frame, there 
being no doubling ? 

Draught, 6.875)1.1111(0.1616 decimal, or proportion of hank, 
6875 last head of drawing. 



42361 
41250 

11111 

6875 



42361 
41250 

1111 



232 HANK, OR PROPORTION OF HANK, ETC. 

If 8 ends be put up at the last head of drawings, and the 
draught be 6.125, and the decimal of the hank 0.1616; what 
decimal, or proportion of hank will the drawings be that are put 
up? 

0.1616 decimal, or proportion of hank at 
8 ends doubling. [last head. 



Draught, 6J, or 6.125)1.2929(0.211 decimal, or proportion of 
12250 hank at middle, or second 

head of drawings. 

6792 
6125 



6679 
6125 

554 



If the hank drawing at second head be 0.211; what will the 
decimal, or proportion of hank be at the first head, if the draught 
be 6.25, and the doubling 8 ? 

0.211 decimal, or proportion of hank at 
8 ends doubling. [middle head. 

Draught, 6J, or 6.25)1.688(0.27 decimal, or proportion of 
1250 hank at first head of draw- 



4380 
4375 



ings. 



If the decimal, or proportion of hank at the first head of draw- 
ings be 0.27, the draught 6.25, and the doubling 8; what decimal, 
or proportion of hank, will the carding be ? 



233 

0.27 decimal of hank at first head of 
8 ends doubling. [drawings. 



Draught, 6|, or 6.25)2.1600(0.3456 decimal of hank card- 
1875 ing. 

2850 
2500 



3500 
3125 



3750 
3750 

If the decimal of the hank-carding be 0.3456, and the draught 
at the carding-engine be 130; what will the decimal of the hank 
lap be? 

Dr't at carding-engine, 130)0.3456(.00265846 decimal, or pro- 

260 portion of hank 

lap. 



856 

780 



760 
650 

1100 
1040 

600 
520 



800 
780 

20 



JV. JB.—The weight of any number of yards of carding or draw- 
ing may be found in the tables, according to the decimal, or 
proportion of hank. 
16 



234 HANK, OR PROPORTION OF HANK, ETC. 

If the decimal, or proportion of the hank lap be 0.00265846, 
and the draught at the lap machine be 2.75, or 2f ; what will 
the decimal, or proportion of the hank of cotton fed on feed-cloth 
at the lap machine be ? 

Draught at lap machine, 2.75)0.00265846(0.0009667 decimal of 

2475 hank fed on feed- 

■ cloth at lap ma- 

1834 chine. 

1650 



1846 
1650 

1960 
1925 



35 

If the decimal, or proportion of hank at the lap machine be 
0.0009667; what will the net weight of cotton fed on 30 inches 
of feed-cloth at the lap machine be? 

Look in the table of dividends for inches, and opposite 30 will 
be found 6.9444 the dividend; which, divided by 0.0009667 the 
decimal, or proportion of hank at the lap machine, will give the 
net weight of cotton in grains. 

Decimal of hank, 0.0009667)6.9444(7183 grs., or 1 ft>., oz., 7 

67669 dwts., 15 grains. 



17754 
9667 

80874 
77336 



35384 
29001 

6383 

N. B. — The above weight being subtracted from the gross weight 
of cotton fed on feed-cloth at lap machine, will give the weight 
of loss sustained in working. 



LOSS IN WORKING. 235 



LOSS IN WORKING. 

Suppose there be 18J- ounces of cotton fed on the feed-cloth 
at the lap machine, and the weight of yarn produced (as appears 
from the preceding example) be 1 ft)., oz., 7 dwts., and 15 
grains; what will the loss sustained in working be? 

oz. dwts. grs. 
18J ounces, = 18 . . 9 . . 2f weight of cotton at lap machine. 
16 . . 7 . . 15 weight of yarn produced. 



2 . . 1 . . llf weight lost in working. 

Or, 

The loss sustained in working any kind of cotton may be found 
in the following manner: — 

Multiply all the draughts together successively for a divisor, 
and all the doublings together accordingly, and that product by 
the numbers of yarn produced for a dividend, and the quotient 
will be the decimal, or proportion of the hank. 

Then look for the dividend in the table opposite the number 
of inches any given weight of cotton is fed on the feed-cloth at 
the lap machine, and divide by the decimal, or proportion of the 
hank, and the quotient will be the net weight in grains ; which, 
subtracted from the weight of cotton fed on the feed-cloth at the 
lap machine, will show the loss sustained in working. 

The loss sustained in each operation maybe ascertained in the 
same manner. 

Suppose the draughts and doubling are as follows : the num- 
bers to be spun 40's, and the weight of cotton fed on 30 inches 
of feed-cloth at the lap machine be 18 J ounces; what will be the 
loss in working ? 

Draught at lap machine, 2.75. 
Draught at carding-engine, 180. 
Draught at 1st head-drawing, 6.25. 
Draught at 2d head-drawing, 6.25. 
Draught at 3d head-drawing, 6.125. 
Draught at slabbing-frame, 6.875. 
Draught at roving-frame, 7.5. 
Draught at mules, 9.6. 



236 loss m working. 

Doubling 1st head-drawing, 8. 
Doubling 2d head-drawing, 8. 
Doubling 3d head-drawing, 8. 
Doubling roving-frame, 2. 

DRAUGHTS. 

2.75 lap machine. 
130 carding-engine. 



8250 

275 



357.50 

6J draught at 1st head-drawing. 



2145.0 

89375 



2234.375 

6J draught at 2d head-drawingo 



13406.250 

55859375 



13964.84375 

6J draught at 3d head-drawing. 



83789.06250 
174560546875 

[to the last head of drawings. 



85534.66796875 total draught from lap machine 
6.875 draught at slabbing-frame. 



42767333984375 
59874267578125 
68427734375000 
51320800781250 

588050.84228515625 



LOSS IN WORKING. 237 

Draughts 1 588050.84228515625 

continued, J 7.5 draught at roving-frame. 

294025421142578125 

411635589599609375 



4410381.317138671875 

9.6 draught at mules. 



26462287902832031250 
39693431854248046875 



Divisor 42339660.6445312500000 total draughts. 

8 doubling 1st head-drawing. 
8 doubling 2d head-drawing. 



64 
8 doubling 3d head-drawing. 



512 

2 doubling roving-frame. 



1024 total doublings. 
40's number spun. 



Dividend 40960 

42339660.64453125)40960.000000000000(0.0009674 decimal, 
38105694580078125 or proportion 

of hank at lap 



28543054199218750 machine. 
25403796386718750 



31392578125000000 
29637762451171875 

17548156738281250 
16935864257812500 

612292480468750 



238 LOSS IN WORKING. 

The dividend for 30 inches is 6.9444, which, divided by 
0.0009674, the decimal or proportion of the hank at the lap 
machine, will give the weight of yarn in grains produced, which, 
subtracted from the 18 J- ounces of cotton fed on the feed-cloth 
at the lap machine, will show the loss sustained in working. 

Dec. or prop, of hank, 0.0009674)6.9444(7178 grains or 16 oz., 

67718 7 dwts., 10 grs. 

of yarn produced 

17264 from 18J oz. of 
9674 cotton. 



75904 
67718 

81864 
77392 



4472 

oz. dwts. grains. 

Cotton consumed at lap machine, 18 . . 9 . . 2f 
Yarns produced, 16 . . 7 . . 10 



Loss sustained in working, 2 . . 1 . . 16f 

The weight of cotton fed on any given length of feed-cloth at 
the lap machine, reduced to grains, may be divided by the 
draughts, and multiplied by the doublings successively, through 
each operation, which will show the gross weight in grains for 
the same length, as the given length of feed-cloth at the lap 
machine, which may be extended to any length, the weight being 
in proportion. 

The net weight of the same length, according to the hank or 
proportion of hank in the same operation, being subtracted from 
the gross weight, will show the loss sustained at each operation, 
or the whole loss throughout the different processes of working. 

iV. B. — Proceed with the same particulars as in the last ex- 
amples. 

If there be 18J ounces of cotton fed on 30 inches of feed- 
cloth at the lap machine, what weight should the same length 



LOSS IN WORKING. 239 

weigh at the different processes (allowing no loss), if the draughts 
and doubling be as follows ? 

DRAUGHTS. 

Lap machine, 2.75, or 2j. 
Car ding-engine, 130. 
1st head of drawings, 6.25, or 6J. 
2d head of drawings, 6.25, or 6J-. 
3d head of drawings, 6.125, or 6J. 
Slabbing-frame, 6.875, or 6J. 
Roving-frame, 7.5, or 7J. 
Mules, 9.6, or 9 T V 

DOUBLING. 

1st head of drawings, 8. 
2d head of drawings, 8. 
3d head of drawings, 8. 
Roving-frame, 2. 

Reduce 18J- ounces to grains for the dividend. 

437.5 grains=l oz. 



18.5, or 18J ounces of cotton fed 
on feed-cloth. 



21875 
35000 
4375 



Draught at lap ma. 2.75)8093.75(2943.2 grs., or 6 oz., 13 dwts. 
550 6i grs., weight of 30 

in. of lap. 



2593 
2475 

1187 
1100 



875 
825 

500 

550 — nearly. 



240 LOSS IN WORKING. 

2943.2 grains, weight of 30 inches of lap ; draught at the card- 
ing-engine 130. 

130)2943.2(22.64 grains, weight of 30 inches 
260 of carding. 



343 

260 



832 
780 

520 

520 

22.64 grains, weight of 30 inches of carding ; draught at the 
1st head of drawings 6.25, and doubling 8. 

22.64 grains, weight of carding. 

8 ends, doubling at 1st head of draw- 
ings. 



Draught, 6.25)181.12(28.9792 grains, or 1 dwt., 4.9792 
1250 grs., weight of 30 inches 
of drawing at the 1st 

5612 head. 

5000 

6120 

5625 

4950 
4375 

5750 

5625 

1250 
1250 



LOSS IN WORKING. 241 

28.9792 grs., weight of drawing 1st head. 
8 ends doubling. 

Draught at 2d ) 

head of draw- V 6.25)231.8336(37.093 grains, or 1 dwt., 13.093 
ings, J 1875 grs., weight of 30 inches 



4433 

4375 



of drawing 2d head. 



5836 
5625 

2110 

1875 

235 

37.093 grains, weight of 30 inches of drawing at 2d head ; 
draught at 3d head of drawings 6.125, and doubling 8. 

37.093 grs., weight of 30 inches of drawing. 
8 ends doubling. 

Draught at } 

3d head of V 6.125)296.746(48.448 grs., or 2 dwts., 0.448 grs., 
drawing, J 24500 weight of 30 inches of draw- 



ing at the third head. 



51746 
49000 

27460 
24500 

29600 
24500 

51000 
49000 

2000 

48.448 grains, weight of 30 inches of drawing at 3d or last head; 
draught at slabbing-frame 6.875 (no doubling). 



242 LOSS IN WORKING. 

Draught at slabbing-frame, 6.875)48.448(7.04698 grains, weight 

48125 of 30 inches 

of slabbing. 

32300 

27500 



48000 
41250 

67500 

61875 



56250 
55000 

1250 

7.04698 grs., weight of 30 in. of slabbing. 
2 ends doubling at roving-frame. 

^ o r v a ^^ e at 17.5)14.09396(1.88 grains, weight of 30 inches 
' * 75 of roving. 



659 
600 



593 

600 — nearly. 

1.88 grains, weight of 30 inches of roving ; draught at mules 
9.6 (no doubling). 

Draught at mules, 9.6)1.88(0.195833 decimal of a grain, weight 
96 of 30 inches of yarn. 



920 

864 




560 

480 


320 

288 


800 
768 


320 

288 



320 32 



LOSS IN WORKING. 243 

0.195833 gr., weight of 30 inches of yarn. 
144, the number of 30 inches in 1 

lea, or 120 yards, 

783333 

783333 
195833 



28.200000 grains, weight of 1 lea. 

25 grains, weight of 1 lea of 40's yarn. 



3.2, or 3^ grains, loss in working 1 lea. 
7 leas, 1 hank. 



22.4 grains, loss in working 1 hank. 
40 hanks, IK). 

grains. 

1 oz. is equal to 437.5)896.0(2 oz., dwts., 21 grains, loss sus- 
8750 tained in working 1ft). 



21.0 



When 30 inches of feed-cloth is the length, any given weight 
of cotton is fed on at the lap machine. The table on the next 
page will show the multipliers for any number of yards weighed 
at any operation. 

The number of grains in any operation, multiplied by the 
figures opposite the number of yards weighed, will give the gross 
weight, from which subtract the net weight. The difference will 
be the loss sustained in working the length weighed. 



244 LOSS IN WORKING. 



TABLE OF MULTIPLIERS. 



For ascertaining the loss sustained in working any given 
length or weight of cotton yarn, as 1 lea, 1 hank, or lib., as 
shown in a preceding example. 



Length weighed. 


Multipli 


Yards. 




1 


1.2 


2 


2.4 


3 


3.6 


4 


4.8 


5 


6 


6 


7.2 


7 


8.4 


8 


9.6 


9 


10.8 


10 


12 


20 


24 


30 


36 


40 


48 


50 


60 


60 


72 


70 


84 


80 


96 


90 


108 


100 


120 


110 


132 


1 lea, or 120 


144 


Leas. 




2 


288 


3 


432 


4 


576 


5 


720 


6 


864 


1 hank, or 7 


1008 



JV. B. — Where 30 inches is the length any given weight of cotton 
is fed on the feed-cloth at lap machine (which is nearly gene- 
ral), the above multipliers answer without exception. 

The proportion of the hank, and the weight of any given 
length, will be sufficiently explained in the foregoing rules, ex- 
amples, and illustrations. However, it will not be out of place 



LOSS IN WORKING. 245 

to give one or two more, as nothing in calculations is more essen- 
tial to masters or managers. 

According to a former example, 30 inches of roving weighs 
1.88 grains (but no person can weigh to so great a nicety). I 
wish to know what 30 yards of the same roving will weigh, and 
what hank it is. 

1.88 grains, weight of 30 inches of roving. 
36 multiplier for 30 yards (see Table). 

1128 
564 



67.68 grains, or 2 dwts., 19.68 grs., weight 
of 30 yards of roving. 

250 is the dividend for 30 yards, which, divided by the number 
of grains it weighs, will give the hank roving. 

grains. Dividend. 
Weight of 30 yards, 67.68)250.00(3.693, or 3 T \ hank rov. nearly. 

20304 



46960 
40608 

63520 
60912 



26080 
20304 

5776 

If the hank roving when weighed be 4J or 4.166 hanks, what 
will be the loss sustained in working 30 yards ? 

250 is the dividend for 30 yards, which, divided by 4.166, the 
hank roving, will give the number of grains net weight. 

Hank roving, = 4.166)250. 000(60 grains, net weight of 30 yards, 
25000 of 4| hank roving, 

N. B. — For loss sustained in working, see next example. 



246 LOSS IN WORKING. 

If the weight of cotton required for 30 yards of roving be 
67.68 grains, and the weight of the same length of roving be 60 
grains, which is equal to 4.166 or 4-J- hanks, what will the loss 
sustained in working be for 1 lea, 1 hank, and 1ft). ? 

67.68 grs., weight of cot. req'd for 30 yds. of rov. 
60 grains, weight of 30 yards of roving. 



7.68 grains, loss at 30 yards. 

4 times 30 is equal to 120 yards, or 1 lea. 



30.72 grains, loss at 1 lea. 
7 leas, 1 hank. 



215.04 grains, loss at 1 hank. 
4.166 hank roving produced. 



129026 
129026 
21504 
86016 



895.85686 grains, loss sustained in working lib. of 

cotton. 

Or, 

1 oz. is equal to 437.5 grs.)895.85686(2.0477 ounces. 

8750 437J grains are 1 oz. 

20856 3339 

17500 1431 
■ 1908 

33568 238 

30625 



20.8687 grains, or 2 oz. 

29436 dwts., 21 grs. 

30625 — nearly. nearly. ! 



AVERAGE COP, ETC. 



247 



AVERAGE COP AND WEIGHT OF SETS. 

To find the numbers of yarn and the number of hanks in one 
set of cops (from an average cop), the weight of the set being 
given. 

RULE. — Multiply the length on one cop by the number of spin- 
dles in the wheels for the number of hanks in the set ; then 
divide by the weight of the set, and the quotient will be the 
numbers of yarn. 

If a set of cops from a pair of wheels containing 808 spindles 
weighs 30 lbs., and the length on one cop be 1 hank, 6 leas, and 
70 threads, what number of hanks will there be in the set, and 
what number of yarn will it be ? 

Leas. Threads. 
6 . . 70 

10xl0x8add8=808spdls. 



Hank. 
One cop contains 1 



Yf£«»\ m . 



19 . 


. 5 . 


. 60 
10 


198 . 


. 1 . 


. 40 

8 


1585 . 
15 . 


. 5 . 
. 6 . 


. 

. = 


160.1 . 


. 4 . 


. ON 



No. of hanks on 1 set 



53.4 nearly, hanks fineness of Nos. of yarn. 

Or, 

Reduce the length on one cop to threads, and multiply by the 
number of spindles in the wheels ; then divide by the number of 
threads in one lea, the quotient of which must be divided by the 
number of leas in one hank, and that quotient will be the number 
of hanks contained in the set; then the number of hanks con- 
tained in the set must be divided by the weight of set, and the 
quotient will be the number of hanks in lib. 



248 



Hank. Leas. Threac 
One cop contains 1 . . 6 . . 70 
7 leas, 1 hank. 

13 

80 threads, 1 lea. 



1110 threads on one cop. 
808 spindles in the pairs of wheels. 



8880 
88800 

1 lea, 8.0 thrds.)89688.0 threads on 1 pair of sets. 



1 hank, 7 leas,)11211 leas on one pair of sets. 

1601.5714 hanks on 1 pair of sets. 
7 leas, 1 hank. 



3.9998 leas. 

80 threads, 1 lea. 



79.9840 threads. 

The length of yarn on one pair of sets will be 1601 hanks, 4 
leas. 

Weight of set, 3.0 Ibs.)160. 1.5714 hanks on one pair of sets. 

53.3857, or rather more than 53J Nos. 

of yarn. 

What will one set of cops weigh, if the wheels contain 808 
spindles, the numbers of yarn 53 hanks to the pound, the num- 
ber of stretches 1000, and the length of the stretch put up 60 
inches? 

Multiply the number of stretches, the length of stretch, and 
the number of spindles in the wheels together respectively for a 
dividend ; then multiply the numbers of yarn by 840 and 36 
respectively for a divisor, and the quotient will be the weight of 
the set. 



AVERAGE COP, ETC. 249 

1000, number of stretches on one cop. 
60 inches, length of stretch. 



60000 
808 number of spindles in wheels. 



48480000 dividend. 

840 yards, 1 hank. 
36 inches,, 1 yard. 

5040 

2520 



30240 inches in 1 hank. 
53, numbers of yarn. 



90720 
151200 



1602720 divisor. 

1602720)48480000(30fts., 3f oz., weight of set. 

4808160 



398400 



16 ounces, IK). 



2390400 
398400 

1602720)6374400(3 ounces. 
4808160 



1566240 

4 qrs., 1 ounce, 



1602720)6264960(3 qrs. 
4808160 



1456800 
17 



250 

What will the weight of one pin or shuttle-cop of 36's weft 
be, containing 450 stretches,*each stretch 57 inches net (allowed 
for breakage). 

450, number of stretches on cop. 
51 inches, length of stretch. 



3150 
2250 



1 yard is 36 inches,)25650(712.5 yards. 

252 



45 

36 



90 

72 

180 
180 



1 lea is 120 yards,)712.5(5.9375 leas on 1 cop. 
600 

1125 
1080 

450 
360 

900 
840 



600 
600 



AVERAGE COP, ETC. 251 

Leas. 

Nos. of weft, 36's)5.937.5(164.93 grains, or 6 dwts., 20.93 grs., 
36 weight on 1 cop. 



233 
216 



177 
144 

335 
324 



110 

108 



How many leas and threads are there in one cop, containing 
712J Jar ds ? 

1 lea is 120 yards,)712.5(5 leas, 75 threads, on 1 cop. 
600 



1J yards is 1 thread, 1.5)112.5(75 threads. 
105 



w 75 
75 

JV. B. — In ascertaining the weight of one cop, reckon your divi- 
dend as many thousands as you have leas; and where the deci- 
mal of a lea occurs, ivhich is generally the case, put the point 
in, reserving the thousands, ivhich, divided by the numbers of 
yarn, will give the weight of the cop in grains. 

What will one cop of 36's twist weigh, containing 900 
stretches, each stretch 61 J inches, exclusive of breakage ? 



252 



900, number of stretches. 
61.5 or 61J inches, length of stretch. 



(6)55350.0 
1 yard is 86 inches, 



( 6)9225 



1 lea is 12.0 yards,)153.7.5 yards on 1 cop. 

12.8125 leas on 1 cop. 

Nos. of yarn, 36)12812.5(355.9 grains, or 14 dwts., 19.9 grains, 
108 weight of 1 cop. 

201 

180 



212 

180 



325 
324 



What will one cop of 48's twist weigh; if it contains 1200 
stretches, each stretch to put up 61 inches, exclusive of breakage? 

1200, number of stretches. 
61 inches, length of stretch. 



1200 
7200 



1 yard is 36 inches, 



(6)73200 inches on 1 cop. 



(6)12200 



1 lea is 12.0 yards,)203.3.3 yards on 1 cop. 

16.944 leas, or 2 hanks, 2.944 leas 
~»™ on 1 cop. 



WEIGHT OF SETS. 253 



Nos. of yarn, 48 < 



Leas. 
f 4)16.944 



(12)4236 



353, grains, or 14 dwts., 17 grains, weight 
of 1 cop. 



WEIGHT OF SETS. 

The number of hanks, and weight of a pair of sets of cops, 
are required from the following particulars: — 

Number of spindles, 1008. 
Number of stretches, 900. 
Length of stretches, 61J inches. 
Numbers of yarn, 36 hanks to 1 lb. 

1008 number of spindles in mules. 
900, number of stretches. 



907200 

61.5, or 61 J inches, length of stretch. 



4536000 
907200 
5443200 



55792800.0 inches of yarn on 1 pair of sets. 

1 yard is 36 inches,)55792800(1549800 yards on 1 set of cops. 
36 

197 

180 

179 
144 

352 
324 

288 
288 



254 WEIGHT OF SETS. 

1 lea is 12.0 yds.)154980.0 yards on 1 set of cops. 



1 hank is 7 leas,)12915 leas on 1 set of cops. 
Nos. of yarn, 



( 6)1845 hanks on 1 set of cops. 
i 6)307.5 



51.25 lbs., or 51 lbs., 4 oz., weight of set. 
16 ounces 1 lb. 

150 
25 



4.00 ounces. 

The number of hanks in a pair of sets of cops is required 
from the following particulars:— 

Number of spindles in mules, 1340. 
Number of stretches, 1200. 
Length of stretches, 59.5 inches. 

1340 spindles in mules. 
1200 stretches. 



1608000 

59.5, or 59J inches, length of stretch. 



8040 
14472 

8040 



1 yd. is 36 in. 



f 6)95676000.0 yards of yarn on 1 set of cops. 
(6)15946000 



1 lea is 12.0 yds.)265766.6.6 yards of yarn on 1 set of cops. 
1 hank is 7 leas,)22147.222 leas of yarn on 1 set of cops. 



3163.888 hanks of yarn on 1 set of cops. 



spinner's book, etc. 



255 



3163.888 hanks of yarn on 1 set of cops. 
7 leas, 1 hank. 



6.222 leas. 

120 yards, 1 lea. 



26.Q66 yards. 



SPINNER'S BOOK, &c. 



Where it is customary to pay the spinners at the rate of so 
much per thousand hanks, the length of the average cop from 
each set may be put down for the week ; then add them together 
and multiply by the number of spindles in the mules, as follows : 













Number of spindles 
in mules. 


Weight 


of sets. 


Average cop. 


lbs. 


oz. 


hanks. 


leas. 


threads. 


1008 


51 


8 




5 


65 




50 


4 




4 


72 




52 


6 




6 


36 




51 


12 




5 


60 




51 


10 




5 


14 




52 


8 




6 


10 




52 


4 




5 


32 




51 


12 




5 


64 




52 


4 




6 


38 




52 


8 




6 


14 




51 







5 





Total for 1 week. 


50 


4 




4 


18 


620 





21 


4 


23 













Hanks. Leas. Threads. 
21 .. 4 .. 23 
7 leas, 1 hank. 



151 

80 threads, 1 lea. 



12103 

1008 spindles in mules. 



96824: 



256 spinner's book, etc. 

96824 
1210300 



Threads in 1 lea, 8.0)1219982.4 threads. 

1 hank is 7 leas,)152497..64, or 152497 leas, 64 threads. 



21785 . . 2 . . 64, or 21785 hanks, 2 leas, 64 
threads, number of hanks on 1 pair of sets of cops. 
Total weight, 620 lbs.)21785(35 J- hanks, average number of yarns. 
1860 



3185 

3100 

85 

The number of hanks per spindle will be ascertained by di- 
viding the number of hanks spun, by the number of spindles in 
the mules, or throstles. 

If the total number of hanks spun in a week be 21745, and 
the number of spindles in the mules be 1008; what number of 
hanks per spindle will be produced ? 

1008)21745(21.5724, or 21 hanks, 4 leas per spindle. 
2016 7 leas, 1 hank. 



1585 4.0068 leas. 

1008 120 yards, 1 lea. 



5770 .8160 
5040 

7300 
7056 

2440 
2016. 

4240 

4032. 

208 



DRESSING MACHINE. 



257 



The spinner's book should be made up so that the weight, num- 
bers of yarn, the total number of hanks, and the number of hanks 
per spindle per week, would appear at one view, for the satisfac- 
tion of the employers, and the government of the managers. 





THE FOLLOWING FORM MIGHT BE ADOPTED 




Date. 
1S39. 

April 
17 


Name. 


Weight, 
lbs. 


Number. 


Total number 
of hanks. 


No. of hanks 
per spindle. 


Rate. 


£ s. d. 


John Pollard. 


620 


35f 


21745 


21.5724 


5. 
3 


2 8 11 



JV. B. — The form of the booh may be altered according to the sys- 
tem of spinning and paying, but the above particulars should 
always appear. 

DRESSING MACHINE. 

Dressing machines are of various constructions, and, like most 
other machines, have been greatly improved ; however, the neces- 
sary calculations will be easily ascertained from the following 
examples. 

The speed of the crank-shaft, on which is fixed the top, or 
large cone drum, is required from the following particulars : — 

Revolutions of driving-shaft a minute, 66. 
Diameter of drum on shaft, 18 inches. 
Diameter of pulley on crank-shaft, 17J inches. 

66 revolutions of driving-shaft a min. 
18, diameter of drum on driving-shaft. 

528 
66 



1188 



258 DRESSING MACHINE. 

on wlTk'-staft '' } 17-5)1188(67.885714 revolutions of crank 
' J 1050 shaft a minute, on which is fixed 

the top, or large cone drum. 

1380 
1225 



1550 
1400 



1500 
1400 

1000 

875 



1250 
1225 

250 
175^ 

750 
700 

50 

The speed of the fan at dressing machine is required from the 
following particulars: — 

Revolutions of crank-shaft a minute, 67.885714. 

Diameter of pulley on crank-shaft for driving fan, 25 inches. 

Diameter of pulley on the end of fan, 2 inches. 

67.885714 revols. of crank-shaft per min, 
25 in., diam. of pul. on crank-shaft. 

339428570 
135771428 



Indiamofpul.| 169 42g50 
on the end of fan, J J _ 



848.571425 revolutions of fan a minute. 

The speed of the fan at dressing machine is required from the 
following particulars : — 



DRESSING MACHINE. 259 

• 
Revolutions of driving-shaft a minute, 66. 
Diameter of drum on shaft, 18 inches. 
Diameter of drum on crank-shaft, 17J inches. 
Diameter of pulley on crank-shaft for driving fan, 25 inches. 
Diameter of pulley on end of fan, 2 inches. 

66 revolutions of driving-shaft a min. 
18 inches, diam. of drum on driving-shaft. 



528 



1188 

25 inches, diam. of pulley on crank-shaft 

for driving fan. 

5940 
2376 



29700 dividend. 



17.5 inches, diameter of pulley on crank-shaft. 
2 inches, diameter of pulley on end of fan. 

35.0 divisor. 

f 5)29700 

35^ 

{ 7)5940 

848.571428 revolutions of fan per minute. 

If the fan of a dressing machine makes 848.571428 revolu- 
tions a minute, and its diameter is 18 inches; how many yards 
will it traverse a minute ? 

848.571428 revolutions of fan a minute. 
1.5 foot, = 18 in. diam. of fan. 



4242857140 

848571428 

1272.8571420 



260 DRESSING MACHINE. 



1272.8571420 

3.1416 circum. when the diam is 1. 



7637142852 

1272857142 
5091428568 
1272857142 
3818571426 



1 yard = 3 feet)3998.8079973072 feet, fan traverses a minute. 

1332.93566576906 yards, fan traverses a min. 

The fan of a dressing machine (as in the above example) will 
traverse a space equal to 1333 yards nearly. 

The speed of the under cone drum is required from the follow- 
ing particulars : — 

Revolutions of crank, or top cone drum-shaft, 67.885714 a min. 
Diameter of top cone drum, llf inches. 
Diameter of bottom cone drum, 4} inches. 

67.885714 revols. of top cone drum-shaft a min. 
11.75, or llf inches, diam. of top cone drum. 



339428570 
475199998 

746742854 



797.65713950 dividend. 

Diam. of under cone drum,4.75in.)797.6571395(167.9278 revols. 

475 of under cone drum 



3226 

2850 


i mm. 


3765 
3325 


3713 
3325 


4407 
4275 


3889 


1321 

950 


3800 



DRESSING MACHINE. 261 

JV. B. — The preceding example shows the greatest speed that the 
under cone drum can ivork ; the largest diameter of the top cone, 
and the smallest diameter of the under cone being given, i. e., 
the greatest speed that can be given to the motions connected 
with the top beam on which the dress yarn is. 

The speed of the top beam can be regulated by a worm, or 
screw-shaft, which works the strap on the drums, and must be 
done according to the heat, or drying, and fineness of yarns. 

The speed of the top, or dressed yarn beam, is required from 
the following particulars. 

Revolutions of under cone-shaft a minute, 167.9278. 

Wheel on the end of cone-shaft, 74 teeth. 

Wheel on foot of upright-shaft, 44 teeth. 

Single worm on top of upright- shaft. 

Wheel on shaft for working top beam, 68 teeth. 

167.9278 revols. of under cone drum a min. 
74 teeth wheel on the end of do. 



6717112 
11754946 



12426.6572 dividend. 

44 teeth, wheel on foot of upright-shaft. 

68 teeth, wheel on shaft for working top beam. 



352 
264 



2992 divisor. 

2922)12426.6572(4.1533 revols. a min. of top, 
11968 or dressed yarn beam, at 

the bottom or beginning. 

4586 
2992 



15945 
14960 



9857 
8976 

8812 
8976— nearly. 



262 DRESSING MACHINE. 

IV. B. — The top, or dressed yarn beam, decreases in speed as it 
fills, continuing to traverse over the same surface as at the com- 
mencement, so that the yarn is dried regularly. 

If the heat, or drying increases, or decreases, which is some- 
times the case, then the top, or dressed yard beam, must be regu- 
lated in speed accordingly, which will be done by moving the 
strap on the cone drums by the worm, or screw attached for that 
purpose. 

PARTICULARS OF DRESSING FRAME. 

Revolutions a min. of crank, or top cone drum-shaft, 67.885714. 

Revolutions of fan a minute, 848.571425. 

Revolutions of under cone a minute, at the bottom of beam, 

167.9287. 
Revolutions of top, or dressed yarn beam a minute, at the bottom 

of beam, 4.1533. 
Diameter of pulley on crank, or top cone drum-shaft, 17J inches. 
Diameter of pulley on crank, or top cone drum-shaft for driving 

fan, 25 inches. 
Diameter of pulley on end of fan, 2 inches. 
Diameter of fan, 18 inches. 
Diameters of top cone drum, llf and 6 inches. 
Diameters of under cone drum, 10J and 4f inches. 
Radius of crank for brushes, 3 inches. 
Radius of crank for leverage, If inch. 
Traversing of fan a minute, 1333 yards, nearly. 

IV. B. — The dimensions of the cone drums are the two extremes. 

What number of ends must there be on each twist beam, allow- 
ing 8 beams to a machine, i. e. 4 beams to each side, to produce 
a piece of cloth 29J inches wide, in a 72 reed, Manchester and 
Stockport count ? 

29.5, width of warp at the end. 
72 reed, Manchester & Stockport count. 



590 
2065 



Number of beams, 8)2124.0 total number of ends in the warp. 
265.5 number of ends on each beam. 



POWER-LOOM. 263 

N. B. — The number of ends required for each beam is 265.5, 
which may be made into 266, and maize two twisters, or double 
ends at the selvage, at each side of the machine. 

What number of ends will it require to produce a top, or dressed 
yarn beam, to fill 51J inches in an 84 reed, Manchester and Stock- 
port count ; and what number of ends must there be on each twist 
beam, allowing 8 twist beams to a machine ? 

51.5 in., width of top, or dres'd yarn bm. at reed. 
84 reed, Manchester and Stockport count. 



2060 
4120 



Num. of bms. 8)4326.0 number of ends in dressed yarn beam. 



540.75 number of ends required on each twist bm. 

JV. B.— Add as many ends as are required, according to the 
number of double ends wanted at the selvages. 

If there be 542 ends on a twist beam, and 8 beams to a ma- 
chine; how many ends will there be in the dressed yarn or top 
beam? 

542 ends on each twist beam. 
8 beams to a machine. 



4336 ends on dressed yarn, or top beam. 

N. B. — The bell wheel at the dressing machine must be regulated 
according to the size of your under roller, and length of piece 
required. 



POWER-LOOM. 

The number of picks a minute is required from the following 
particulars : — 

Revolutions of driving-shaft a minute, 102. 
Diameter of drum on driving-shaft, 14 inches. 
Diameter of pulley on loom, 11 inches. 



264 POWER-LOOM. 



102 revols. of driving-shaft a min. 
14 in. diam. of drum on same shaft. 



408 
102 



In. diam. of pul. on loom, 11)1428 



129.818 number of picks a min. 

If the crank-shaft of a loom makes 129.818 revolutions a 
minute, with a wheel 50 teeth fixed on the end, working into a 
wheel with 100 teeth on the end of the tappet-shaft; what num- 
ber of revolutions will the tappet-shaft make a minute ? 

129.818 revolutions of crank-shaft a min. 
50 teeth on end of crank-shaft. 



Teeth on end of 1 100)6490J00 
tappet-snatt, J ' 

64.909 revolutions a min. of tapt. -shaft. 

N.B. — The above examples only refer to plain cloths, but the 
calculations of twills, fustians, and all other fancy goods, are 
regulated by the number or different constructions of the tappets 
working upon the treadles, or levers, connected with the healds, 
whereby nearly any pattern may be constructed and manufac- 
tured as by hand-weaving. 

The number of picks a minute is required from the following 
particulars :— 

Revolutions of driving-shaft a minute, 98.25 
Diameter of drum on driving-shaft, 15.5 inches. 
Diameter of pulley on crank-shaft, 12.75 inches. 

98.25 revolutions of driving-shaft a minute. 
15.5, or 15J in. diam. of drum on driving-shaft. 



49125 
49125 

9825 



1522.875 dividend. 



POWER-LOOM. 265 

Inches diam of pulley ) 12 . 7 5)1522.875(119.441 revolutions of 
on crank-shaft, 12|, $ ^ crank-shaft 



a minute. 



2478 
1275 

12037 
11475 



5625 
5100 

5250 
5100 

1500 
1275 

225 

The speed of the tappet-shaft is required from the following 
particulars :— 

Revolutions of crank-shaft a minute, 119.441. 
Wheel on end of crank-shaft, 50 teeth. 
Wheel on end of tappet-shaft, 100 teeth. 

119.441 revols. of crank-shaft a min. 
50 teeth, wheel on crank-shafts 



Whl. on tapt-shft. 100 tth.)5972.050 

59.7205 revolutions of tappet-shaft 

a minute. 

If the crank-shaft of a power-loom makes 129.818 revolutions, 
i. e. picks, a minute; what time will be required to work suc- 
cessively, to produce a piece of cloth 29 yards long, with $8 
picks, or threads in 1 inch? 
18 



266 POWER-LOOM. 



29 yards, length of piece. 

37 inches, length hooked for 1 yard. 



203 
8T 



1073 number of inches in 1 pick. 
88 number of picks in 1 inch. 

8584 
8584 



Dividend 94424 total number of picks in 1 piece, 

29 yards long. 

Num. of picks a min., 129.818)94424.00(727.3567 mins. required 

908726 to work successively, 



to produce 1 piece of 
355140 cloth, 29 yards long, 
259636 or 12 hours, 7 mins., 
— 21.402 seconds. 

955040 

908726 



463140 
389454 

736860 
649090 

877700 
778908 



987920 
908726 

79194 



The length of time required for the loom to work successively? 
to produce 1 piece of cloth 29 yards long with 88 picks, or 
threads in 1 inch, will be 12 hours, 7 minutes, and 21 seconds. | 

N. B. — The distance of the hooks on all frames for hooking pieces 
is 37 inches, 



POWER-LOOM. 267 

If the crank-shaft of a power-loom makes 119.441 revolutions 
a minute, i. e. so many picks or threads; what length of time 
must it work successively, to produce a piece of cloth 29 yards 
long with 84 picks, or threads in 1 inch? 

29 yards, length of piece. 

37 inches, length hooked for 1 yard. 

203 

87 



1073 number of inches in 1 piece of cloth. 
84 number of picks or threads in 1 inch. 



4292 
8584 



Dividend 90132 number of picks in 1 piece of cloth 29 

yards long. 

Num. of picks a min., 119.441)90132.0(754.615 minutes, or 

836087 60)754.615 



652330 12.. 34.. 615 
597205 60s.lm. 



551250 36.900 

477764 



734860 
716646 

182140 
119441 



626990 
597205 

29785 

The length of time required for the loom to work successively, 
to produce a piece of cloth of the foregoing description, will be 
12 hours, 34 minutes, 37 seconds, nearly. 

The weight of yarn is required, to make one piece of cloth, of 
the following description : — 



268 



POWER-LOOM. 



Length of piece, 29 yards. 

Count of reed, 72. (Manchester and Stockport count.) 

Numbers of twist, 36's. 

Width of warp at the reed, 29 J- inches. 

Number of picks in 1 inch, 88. 

Number of weft, 36's. 

29 yards, length of piece. 
72, Manchester and Stockport count of 
— — reed. 



58 
203 



2088 



29J inches, width of warp at the reed. 



18792 
4176 
1044 



1 hank is 840 yards,)61596(73.328 hanks of twist required for 
5880 the piece. 



2796 
2520 

2760 
2520 



2400 

1680 



7200 
6720 

480 



29 yards, length of piece. 
88 picks or threads in 1 inch. 



232 
232 



2552 
29.5, or 29J inches, width at the reed. 



12760 



POWER-LOOM. 269 

12760 
22968 
5104 

75284.0 

1 hank is 840 yards,)75284.0(89.624 hanks of weft required 
6720 for the piece* 



8084 
7560 



5240 

5040 

2000 

1680 

3200 
3360— nearly. 

73.328 hanks of twist. 
89.624 hanks of weft. 



I 



( 6)162.952 hanks of yarn required for 1 

Numbers of yarn, 36 i piece. 

6)27.158 

4-526 Bbs. of yarn, 
16 oz., 1ft). 

3156 

526 

8.416 ounces. 

4 qrs. 1 ounce. 



1.664 qrs. 

The weight of yarn required for the piece is 4 lbs. 8J oz., 
nearly^ 

Or, 

When the numbers of twist and weft are the same, the question 
may be worked in one operation, by adding the Manchester or 



270 POWER-LOOM. 

Stockport count of reed, and the number of picks, or threads re- 
quired in the inch together, and then proceed as in either of the 
last examples. 

Thus, 

72, Manchester or Stockport count of reed. 

88 picks, or threads in 1 inch. 

160 
29 yards, length of piece. 



1440 
320 



4640 

29.5 inches width at the reed. 



23200 
41760 

9280 



136880.0 dividend. 



Yards in 1 hank, 840 
Numbers of yarn, 36 



5040 
2520 



Yards inl ft., 30240)136880.0(4.526 lbs. of yam 
120960 



159200 
151200 



80000 
60480 

195200 
181440 

13760 

The weight of yarn required for the piece is 4 lbs., 8| oz. 
nearly as in the last example. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 271 



THE DRIVING AND DRIVEN WHEELS REQUIRED TO PRODUCE ANY 
GIVEN DRAUGHT BETWEEN THE MIDDLE AND BACK ROLLERS, 
AND BETWEEN THE BACK AND FRONT ROLLERS, THE DIAMETER 
OF THE ROLLERS BEING GIVEN. 

WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT FOR BACK 
AND MIDDLE ROLLERS. 

RULE. — Multiply the length you intend drawing, by the di- 
ameter of the middle roller, for the driving-wheel ; and the length 
you wish that drawn into, by the diameter of the back roller, for 
the driven-wheel. 

If a greater or less number of teeth be required in the wheel, 
divide the driver and driven-wheels by any number that will di- 
vide both without a remainder ; then multiply the quotients by 
any number, according to the number of teeth wanted in the 
wheels. 

N. B. — The diameter of the wheels will be according to the pitch 
of the teeth. 

What number of teeth must there be in the wheel required, 
for the back and middle rollers to produce a draught of 1 into 2, 
allowing the back roller to be J inch, and middle roller 1 inch 
in diameter ? 

1 into 2 draught 
Middle roller 1 inch, or 8 7, or J inch back roller. 

Divided by 2)8 14 

Quotients 4 and 7 
Multipliers 5 5 

Mid. rol., driving-wheel 20tth. 35 teeth, driven-wheel. 

Required the draught between the middle and back rollers, 
from the following particulars : — 

Wheel on middle roller, (driving-wheel,) 20 teeth. 
Wheel on back roller, (driven-wheel,) 35 teeth. 
Diameter of middle roller, 1 inch. 
Diameter of back roller, J inch. 



272 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

Driving-wheel. Driven-wheel. 

In diam of ) ^ teeth. 35 teeth, 

back Poller'., §[ J__ 1 inch ' °^ diam - of middle rol. 

140 140)280(2, or 1 into 2 draught, 

280 between middle and 

back rollers. 

What number of teeth must there be in the wheels on the back 
and middle rollers, to produce a draught equal to 2 into 3, if the 
back roller be J inch, and the middle roller 1 inch in diameter? 

2 into 3 draught, 
Middle roller, 1 inch, or 8 7, or J inch back roller. 

Middle roller wheel, 16 21 wheel on back roller. 

2 2 

Middle roller wheel, 32 tth. 42 teeth, wheel on back roller. 

The draught between the middle and back rollers is required 
from the following particulars: — 

Driving-wheel. Driven-wheel. 
16 teeth. 21 teeth. 
Diameter of back roller, 7 8, or 1 inch diam. of mid. rol. 



112 )168(1.5, or 2 into 3 draught. 

112 



560 
560 



Or, 

Driving-wheel. Driven-wheel. 
32 teeth. 42 teeth. 
Diameter of back roller, 7 8, or 1 in. diam. of mid. rol, 



224 )336(1.5, or 2 into 3 draught. 

224 

1120 

1120 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 273 

What number of teeth must there be in the wheels on the back 
and middle rollers, to produce a draught equal to 3 into 4, if the 
back and middle rollers be the same diameters ? 

3 into 4 draught. 

Middle roller wheel, 21tth.28 teeth, back roller wheel. 

The draught between the middle and back roller is required 
from the following particulars, the diameters of the rollers being 
the same: — 

Driving-wheel. Driven-wheel. 

21 21)28(11 or 3 into 4 draught, 

21 



7 
21 



The wheels for the back and middle rollers are required to pro- 
duce a draught of 3 into 4, the diameter of the back roller being 
1 inch, and the middle roller 1 j- or f inch diameter : — 

3 into 4 draught. 
Middle roller, f inch 9 8, or 1 inch back roller. 

27 tth. 32 teeth, wheel for back roller. 

The draught between the middle and back rollers is required 
from the following particulars : — 

Wheel on middle roller, 27 teeth. Diam. of middle roller, 1 J inch. 
Wheel on back roller, 32 teeth. Diameter of back roller, 1 inch. 

Driving-wheel. Driven-wheel. 

27 teeth. 32 teeth. 
Back roller 1 inch, or 8 9, or 1J inch, middle roller. 



216 )288(li or 3 into 4 draught, 

216 

72 

216 ~° 3 



274 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

What wheels will be required to produce a draught of 4 into 
5, between the middle and back rollers, if the back roller be -J 
inch, and the middle roller 1 inch diameter ? 

4 into 5 draught. 
Middle roller, 1 inch, or 8 7, or { inch back roller. 

Middle roller wheel, 32 tth. 35 teeth, wheel back roller. 

The draught between the back and middle rollers is required 
from the following particulars : — 

Wheel on middle roller, 32 teeth. Diam. of middle roller, 1 inch. 
Wheel on back roller, 35 teeth. Diameter of back roller, -J inch. 

Driving-wheel. Driven-wheel. 
32 teeth. 35 teeth. 
Back roller, | inch or 7 8, or 1 inch, middle roller. 



224 )280(1.25, or 4 into 5 draught. 

224 



560 
448 

1120 
1120 

What wheels will be required to produce a draught of 5 into 
6, between the middle and back rollers, if the back roller be J 
inch and the middle roller 1 inch diameter ? 

5 into 6 draught. 
Middle rollers, 1 inch or 8 7, or J inch, back roller. 

Divide by 2)40 tth. 42 teeth, wheel back roller. 
— or — 
Middle roller wheel, 20 tth. 21 teeth, wheel back roller. 

The draught between the middle and back rollers is required 
from the following particulars : — 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 275 

Driving-wheel. Driven-wheel. 
40 teeth. 42 teeth. 
Back roller, J inch, or 7 8, or 1 inch, middle roller. 



280 )336(1.2 or 5 into 6 draught. 

280 



560 
560 



N. B. — The wheels may be reduced to 20 and 21, and the draught 
will be the same. 

What wheels will be required to produce a draught of 6 into 
7, between the middle and back rollers, if the back roller be f 
inch and the middle roller 1 inch diameter ? 

6 into 7 draught. 
Middle roller 1 inch or 8 7, or J inch back roller. 

Middle roller wheel, 48 tth. 49 teeth, wheel on back roller. 

If there be a wheel 48 teeth on Ihe middle roller, working into 
a wheel 49 teeth on the back roller, and the back roller be J inch, 
and the middle roller 1 inch diameter ; what will the draught be ? 

Driving-wheel. Driven-wheel. 
48 teeth. 49 teeth. 
Back roller, J inch, or 7 8, or 1 inch middle roller. 

336 )392(li, or 6 into 7 draught. 

336 



56 



336 



What wheels will it require to produce a draught between the 
middle and back rollers of 7 into 8, if the back roller be | inch, 
and the middle roller 1 inch diameter ? 



276 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

7 into 8 draught. 
Middle roller, 1 inch, or 8 7, or | inch back roller. 

Divided by 8)56 56 

Lowest number 7 7 lowest number. 

3 3 

Middle roller wheel 21 tth. 21 teeth, wheel back roller. 

The draught between the middle and back rollers is required 
from the following particulars : — 
Wheel on the middle roller 21 teeth, working into wheel on stud 

40 teeth, which works wheel 21 teeth on back roller. 
Diameter of the middle roller 1 inch, and diameter of the back 
roller J inch. 

Driving-wheel. Driven-wheel. 
21 teeth. 21 teeth. 
Back roller, | inch 7 8, or 1 inch, middle roller. 



147 )168(li, or 7 into 8 draught. 

147 

21 

147 

What wheels will be required for the middle and back rollers, 
to produce a draught of 7 into 8 ; allowing the back and middle 
rollers to be the same diameters ? 

7 into 8 draught. 

2 2 

Middle roller wheel, 14 tth. 16 teeth, wheel back roller. 

Or, 
7 into 8 

3 3 

Middle roller wheel, 21 tth. 24 teeth, wheel back roller. 
Or, 
7 into 8 

4 4 

Middle roller wheel, 28 tth. 32 teeth, wheel back roller. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 277 

The draught between the middle and back rollers is required 
from the particulars in the last example : — 

Driving-wheel. Driven- wheel, 
teeth. 
14 teeth,)16(14, or 7 into 8 draught. 
14 

2 
— or 4. 
14 

21 teeth, )24(li, or 7 into 8 draught. 
21 



3 
21 



— or 4< 



28 teeth,)32(l*, or 7 into 8 draught. 

28 

4 

— or 4» 

28 

What wheels must there be on the middle and back rollers, to 
produce a draught of 8 into 9, if the back roller be J inch, and 
the middle roller f inch diameter? 

8 into 9 draught. 
Middle roller, f inch, or 6 7, or J inch, back roller. 

Middle roller wheel, 3)48 tth. 63 teeth, back roller wheel. 

Middle roller wheel, 16 tth. 21 teeth, back roller wheel, 

2 2 

Middle roller wheel, 32 tth, 42 teeth, back roller wheeh 

The draught between the middle and back rollers is required 
from the following particulars :— 



278 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

Driving-wheel. Driven-wheel. 
Wheel on middle roller, 32 teeth. 42 teeth, wheel on back roller. 



224 )252(1J, or 8 into 9 draught. 

224 



28 

or J. 



224 



What wheels will be required to produce a draught of 9 into 
10, between the middle and back rollers, allowing the back and 
middle rollers to be the same diameter ? 

9 into 10 draught. 

2 2 

Wheel on middle roller, 18 tth. 20 teeth, wheel on back roller. 

Or, 

9 into 10 

3 3 

Wheel on middle roller, 27 tth. 30 teeth, wheel on back roller. 

Or, 

9 into 10 

4 4 

Wheel on middle roller, 36 tth. 40 teeth, wheel on back roller. 

If there be a wheel 40 teeth on back roller, and a wheel 36 
teeth on middle roller; what draught will there be if the middle 
and back rollers are the same diameter ? 

teeth. 
Wheel on middle roller, 36 teeth. )40(1J, or 9 into 10 draught. 

36 



or f 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 279 

If the back roller be 1 inch, and the middle roller J inch di- 
ameter ; what wheels will be required to produce a draught of 9 
into 10, between the middle and back rollers? 

9 into 10 
Middle roller, J inch, or 7 8, or 1 inch, back roller. 

Middle roller wheel, 63 tth. 80 teeth, wheel back roller. 

The draught between the middle and back rollers is required 
from the following particulars: — 

Wheel on middle roller, 63 teeth. Wheel on back roller, 80 tth. 
Diameter of middle roller, J inch. Diameter of back roller, 1 in. 

Driving-wheel. Driven-wheeL 
63 teeth. 80 teeth. 
Back roller, 1 inch, or 8 7, or j inch middle roller. 



504 )560(1}, or 9 into ten draught. 

504 



56 
__i 

504 



If the back roller be f inch, and the middle roller f inch di- 
ameter ; what wheels will be required to produce a draught of 10 
into 11, between the middle and back rollers? 

10 into 11 
Middle roller, f inch, or 6 7, or | inch, back roller. 

Middle roller wheel, 60 tth. 77 teeth, wheel on back roller. 

Or, 
If the back and middle rollers were the same diameter. 

10 inch 11 

2 2 

Middle roller wheel, 20 tth. 22 teeth, wheel on back roller, 



280 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

Or, 

10 into 11 
3 3 

Middle roller wheel, 30 tth. 33 teeth, wheel on back roller. 

If the wheel on the back roller be 77, and the wheel on the 
middle roller 60, and the back roller f inch, and the middle 
roller f inch diameter, required the draught? 

Driving-wheel. Driven-wheeh 
60 teeth. 77 teeth. 
Back roller, J inch, 7 6, or f inch, middle roller. 



420 )4t*2(l.l, or 10 into 11 draught. 

42(^ 



TOTAL DRAUGHT IN ROLLERS. 

RULE.— Multiply the diameter of the front roller by any num- 
ber that will produce a wheel of a sufficient diameter for the first 
driving; then multiply the diameter of the back roller by twice 
the number the front roller is multiplied by for the first driven 
wheel, which will produce a draught equal to 2. If a draught 
of 3 be required, multiply the diameter of the back roller by 3 
times the number by which the front roller is multiplied; if any 
intermediate draught between the whole numbers be required, as 
2J, 2 J, or 2 J, add to the product in proportion; and if above 3 
of a draught be required, proceed accordingly. 

The first driving and driven-wheels being ascertained, divide 
the total draught required by the draught produced ; the quotient 
of which, multiplied by the second driving wheel, will give the 
second driven-wheel ; if more wheels are required, they will be 
found in the same way. 

JST.B. — -The second driving, or change-wheel may contain any 
number of teeth, according to the diameter required. 

If larger or smaller wheels be required, they may be increased, 
or decreased, in proportion to each other, i. £., the driving and 
driven-wheels must be multiplied, or divided by the same number. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 281 

If the back roller be 1 inch, and the front roller 1J inch 
diameter ; "what wheels will be required to produce a draught of 6 ? 

Diameter of front roller, 9, or 1J- inches. 

3 

First-driving wheel, 27 teeth. 

Diameter of back roller, 8, or 1 inch. 
3 x 2 = 6 

First-driven wheel, 48 teeth. 

Driving-wheel. Driven-wheel. 
27 teeth. 48 teeth. 
Back roller, 1 inch, or 8 9, or 1J inch, front roller. 



216 )432(2 draught. 
432 

2)6 total draught. 



3 

2d dving. or change-whl., 24 teeth. 



2d driven-wheel, 72 teeth. 



The draught is required from the following particulars : — 

Driving-wheels, 27, and 24. Driven-wheels, 48, and 72. 
Diameter of back roller, 1 inch, and front roller, 1J, or § inch, 

Driving-wheels. Driven-wheels. 
27 teeth. 48 teeth. 
24 teeth. 72 teeth. 



108 96 

54 336 



648 3456 

Diam. back roh, 1 in., or 8 9, or 1 J inch, diam. front rol. 



5184 )31104(6 draught required. 
31104 
19 



282 WHEELS REQUIRED TO PRODUCE ANY GIVEN DKAUGHT. 

Note. — Speeds, draughts, S^c, may be wrought with fewer figures 
by the following method of cancelling, viz., place all the driven- 
wheels and the diameter of the front rollers as numerators, and 
all the driving-wheels and the diameter of the back rollers as 
denominators ; then proceed by dividing with any number that 
will divide both numerator and denominator without any re- 
mainder, and the results of the numerators multiplied together 
for a dividend, and the results of the denominators for a divi- 
sor, and the quotient will be the answer required. 

If the driving-wheels are 27, and 24, and the diameter of the 
back roller 1 inch, and the driven- wheels are 48, and 72, and the 
diameter of the front roller 1 J inch ; what will the draught be ? 

6 3 

48 x 72 X 9 6 or 6 draught. 



27 24 

9 



If the back roller be -J inch, and the front roller 1 inch diame- 
ter; what wheels will be required to produce a draught of 5J? 

Diameter of front roller, 8, or 1 inch. 

3 

First driving-wheel 24 teeth. 

Diameter of the back roller 7, or J inch. 
3 x 2=6 

First driven-wheel, 42 teeth. 

Driving-wheel. Driven-wheel. 
24 teeth. 42 teeth. 
Back roller, | inch, or 7 8, or 1 inch, front roller. 



168 )336(2 draught. 

336 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 283 

2)5.5 total draught. 



2.75 
2d driving, or change-wheel, 28 teeth. 

2200 
550 



2d driven-wheel 77.00 teeth. 

If the driving-wheels he 24, and 28, the diameter of the hack 
roller J inch, and the driven-wheels 42, and 77, and the diame- 
ter of the front roller 1 inch, what will the draught be ? 



Driving-wheels. Driven-wheels. 
24 teeth. 42 teeth. 
28 teeth. 77 teeth. 


192 

48 


294 
294 


672 
Back roller, J inch, or 7 


3234 

8, or 1 inch, front roller 


4704 


)25872(5.5, or 5J draught. 
23520 




23520 
23520 



If the hack roller he J inch, and the front roller 1 inch diame- 
ter ; what wheels will be required to produce a draught of 2 J in 
the first driving and driven-wheels, and a total draught of 7 ? 

Diameter of front roller, 8, or 1 inch. 

3 

First driving-wheel, 24 teeth. 

Diameter of back roller, 7, or J inch. 
3 x 2 = 6 

42 

Add 21 divided by 3 = 7 

First driven-wheel, 49 teeth 



284 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT, 

Driving-wheel. Driven-wheel. 
24 teeth. 49 teeth. 
Back roller, | inch, or 7 8, or 1 inch, front roller. 

168 )392(2J draught. 

336 



56 

168 



-i 



2J- draught. 7, total draught, 
3 3 

7 7)21 



21 second driving or change-wheel. 
63 second driven-wheel. 

If the driving-wheels be 24, and 21, and the driven-wheels 49, 
and 63, the back roller J inch, and the front roller 1 inch diame- 
ter ; what will the draught be ? 

Driving-wheels. Driven-wheels. 
24 teeth. 49 teeth. 
21 teeth. 63 teeth. 

24 147 

48 294 



504 3087 

Back roller, J inch, or 7 8, or 1 inch, front roller; 



3528 )24696(7 draught. 
24696 

If the diameter of the front roller be 1J- inch, and the back 
roller 1 inch ; what wheels will be required to produce a draught 
of4|? 

Diameter of the front roller, 9, or 1 J inch. 

2 

First driving- wheel 18 teeth. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 285 

Diameter of back roller, 8, or 1 inch. 
2 x 2=4 

First driven-wheel, 32 teeth. 

Driving-wheel. Driven-wheel. 
18 teeth. 32 teeth. 
Back roller, 1 inch, or 8 9, or 1J- inch, front roller. 



144 )288(2 draught. 

288 

2)4.5 total draught. 



2.25 
2d driving-wheel, 28 teeth. 



1800 
450 



2d driven-wheel, 63 teeth. 

The draught in rollers is required, when the driving-wheels are 
18, and 28, and the driven wheels 32, and 63, and the diameter 
of the back roller 1 inch, and front roller 1J inch. 

Driving-wheels. Driven-wheels. 
18 teeth. 32 teeth. 
28 63 



144 

36 

504 
Back roller, 1 inch, or 8 


96 
192 

2016 

9, or 1 J inch front roller 


4032 


)18144(4.5, or 4J draught. 
16128 




20160 
20160 



286 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

What wheels will be required to produce 7J draught, if the 
back roller be 1 inch diameter, and the front roller 1 J inch ? 

Diameter of front roller, 1J inch, =9 

3 

First driving-wheel, 27 teeth. 

Diameter of back roller, 1 inch, or 8 

3 x 2 = 6 

48 
Add 24 divided by 2 for one-half =12 

First driven-wheel, 60 teeth. 

Driving-wheel. Driven-wheel. 
27 teeth. 60 teeth. 
Diam. of back rol. 1 in., or 8 9, or 1 J in. diam. of front rol. 



216 )540(2.5, or 2| draught. 

432 



1080 
1080 



7J is the total draught required, which must be divided by 2J- 
the first draught ; the quotient of which multiplied by the second 
driving or change-wheel, will give the second driven-wheel. 

Thus, 

2.5)7.5(3 multiplied by wheel 26 teeth, will 
75 be equal to 78 teeth, wheel 2d 
— driven. 

The draught in rollers, is required from the following particu- 
lars: — 

Driving-wheels, 27, and 26 teeth. Driven-wheels, 60, and 78 tth. 
Back roller, 1 inch diameter; and front roller, 1J inch. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 287 



Driving-wheels. 
27 teeth. 
26 teeth. 


Driven-wheels. 
60 teeth. 
78 teeth. 


162 
54 


4680 

9, or 1J inch, front rol. 


702 
Bk. rol. 1 in., or 8 


42120 dividend. 


5616 divisor. 




5616)42120(7.5, 
39312 


or 7J draught. 


28080 
28080 




Or, 




BY CANCELLING. 


15 S 




60 78 


9 15 


27 26 


— = ■ — asa 7J draught. 
8 2 


9 


2 



If the diameter of the front roller be 1 inch, and the back 
roller J inch ; what wheels will be required to produce a draught 
of 8? 

Diameter of front roller, 1 inch, or 8 

3 



First driving-wheel, 24 teeth. 

Diameter of back roller, J inch, or 7 

3 x 2 = 6 

First driven-wheel, 42 teeth. 



288 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

Driving-wheel. Driven-wheel. 
24 teeth. 42 teeth. 
Back roller, J inch, or 7 8, or 1 inch, front roller. 



168 )336(2d draught. 

336 

2)8 total draught. 

4 
2d driving-wheel, 20 teeth. 

2d driven-wheel, 80 teeth. 

If the driving-wheels be 24, and 30, and the driven-wheels 42, 
and 80, the back roller J inch diameter, and the front roller 1 
Inch; what will the draught be? 

Driving-wheels. Driven-wheels. 
24 teeth. 42 teeth. 
20 teeth. 80 teeth. 



480 3360 
Diam. of bk. rol., | in., or 7 8, or 1 in. diam. of front rol. 



3360 )26880(8 draught at rollers. 
26880 

If the diameter of the back roller be | inch, and the front 
roller 1 inch; what wheels will be required to produce a draught 
of 9, i. e., 1 into 9? 

Diameter of front roller, 8, or 1 inch. 

3 

1st driving-wheel, 24 teeth. 

Diameter of back roller, 7, or j inch. 
3 x 2 = 6 

42 

Add 21 divided by 3 = 7 

1st driven-wheel, 49 teeth. 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 289 

Driving-wheel. Driven-wlieel. 
24 teeth. 49 teeth. 
Back rollers, J inch, or 7 8, or 1 inch front roller. 





168 )392(2J draught 
336 


% 


56 

168 


2 J draught 
3 


9 total draught. 
3 


7 


7)27 




26 



2d driving-wheel, 21 teeth. 

2d driven-wheel, 81 teeth. 

The draught in rollers, is required from the following par- 
ticulars: — 

Driving-wheels, 24, and 21 teeth. Diameter of back roller, J inch. 
Driven-wheels, 49, and 81 teeth. Diameter of front roller, 1 inch. 

Driving-wheels. Driven-wheels. 
24 teeth. 49 teeth. 
21 teeth. 81 teeth. 

24 49 

48 392 



504 3969 

Back roller, -J inch, or 7 8, or 1 inch, front roller. 



3528 )31752(9 draught, 
31752 



290 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 

If the diameter of the back roller be 1 inch, and the front 
roller 1J- inch, what wheels will be required to produce a draught 
of 2J, between the first driving and driven-wheels, and a total 
draught of 8.4375? 

Diameter of front roller, 9, or 1J inch. 

3 



1st driving-wheel, 27 teeth. 

Diameter of back roller, 8, or 1 inch. 
3 x 2 = 6 

48 
Add 24 divided by 4 =6 

1st driven-wheel, 54 teeth. 

Driving-wheels. Driven-wheels. 
27 teeth. 54 teeth. 
Diam. back rol., 1 in., = 8 9, or lj- inch, front roller. 



Divisor 216 486 dividend. 

216)486(2.25, or 2J- draught, between the first 
432 driving and driven-wheels. 

540 
432 



1080 
1080 



Draught required. 
1st draught, 2.25)8.4375(3.75 = 2d draught. 
675 

1687 
1575 

1125 
1125 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 291 

3.75, 2d draught. 
2d driving, or change-wheel, 24 teeth. 

1500 

750 



90.00 2d driven wheel, 90 teeth. 

The draught in rollers is required from the following particu- 
lars: — 

Driving-wheels, 27, and 24 teeth. Diameter of hack roller, 1 inch. 
Driven-wheels 54, and 90 teeth. Diameter of front roller 11 inch. 



Driving-wheels. Driven-wheels. 
27 teeth. 54 teeth. 
24 teeth. 90 teeth. 

108 4860 

54 9, or 1J inch, 


front roller. 


648 43740 dividend. 
Back rollers, 1 inch, or 8 

5184 divisor. 

5184)43740(8.4375 draught required. 
41472 


22680 
20736 




19440 
15552 




38880 
36288 




25920 
25920 





If 5J hank roving produces No. 45's twist, what will the total 
draught at the mules be ? 



292 WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 



Hank 


roving, 5J 


45's No. 


of twist. 




3 


3 






16 


)135(8.4375 
128 

70 


draught 






64 


120 
112 






60 








48 


80 
80 



mules. 



JV. B. — When there are any fractional parts in the divisor , or 
dividend, reduce them to the same name as in the last example. 

If the diameter of the back roller be J inch, and the front 
roller 1 inch, what wheels will be required to produce a draught 
of lOf, or 10,666; the draught between the first driving and 
driven-wheels to be 2f , or 2.666. 

Diam. of front rol., 1 inch, or 8. Diam. of bk. rol. j inch, of 7 

3 3x2=6 

1st driving-wheel, 24 teeth. 42 

Add f of 21 = 14 

1st driven- wheel, 56 tth. 

Driving-wheel. Driven-wheel. 
24 teeth. 56 teeth. 



Back roller £ inch, or 7 


8, or 1 inch front roller. 


168 


)448(2.66, first draught. 
336 




1120 

1008 




1120 

1008 



112 



WHEELS REQUIRED TO PRODUCE ANY GIVEN DRAUGHT. 293 

Draught required. 
1st draught, 2.66)10.66(4, 2d draught. 
1066 
2d driving, or change-wheel, 22 teeth. 

4, 2d draught. 

2d driven-wheel, 88 teeth. 

The draught between the back and front rollers of a throstle, 
is required from the following particulars : — 

Driving-wheels, 24, and 22 teeth. 
Driven-wheels, 56, and 88 teeth. 
Diameter of back roller, § inch. 
Diameter of front roller, 1 inch. 

Driving-wheels. Driven-wheels. 
24 teeth. 56 teeth. 
22 teeth. 88 teeth. 



48 448 

48 448 



528 4928 

Back roller, | inch, or 7 8, or 1 inch, front roller. 



3696 )39424(10.66, or lOf, draught be- 
3696 tween back and front 

• ■ rollers of the throstle, 

24640 

22176 



24640 

22176 

2464 



EXPLANATION TO THE REED TABLE. 

1. Manchester and Stockport count by the number of ends in 

1 inch. 

2. Bolton counts by the number of beers on 24J inches, 20 

dents to a beer. 

3. Blackburn counts by the number of beers on 45 inches? 20 

dents to a beer. 



294 EXPLANATION TO THE REED TABLE. 

4. 6-4ths Preston counts by the number of beers on 58 inches* 

20 dents to a beer. 

5. 9-8ths Preston counts by the number of beers on 44 inches, 

20 dents to a beer. 

6. 4-4ths Preston counts by the number of beers on 39 inches, 

20 dents to a beer. 

7. T-8ths Preston counts by the number of beers on 34 inches, 

20 dents to a beer. 

8. Nankeen counts by the number of beers on 20 inches, 19 

dents to a beer. 

9. Scotch and Carlisle count by the number of dents on 37 

inches. 

10. Silk counts by the number of ends on 36 inches. 

11. Number of dents in 1 yard. 

12. The United States of America, the number of splits or dents 

in a reed 36 inches wide, indicates the count of cloth in 
the States of Pennsylvania, New Jersey and Delaware, 
and throughout nearly all the States for all twilled goods, 
but plain goods are counted by the number of threads on 
an inch, each split or dent containing 2 threads. For 
instance, 

If we wish to determine the count of any particular 
plain goods, we count the number of threads on an inch, 
and that number multiplied by 36, and divided by 2, gives 
you the reed on which the goods were woven. 

In setting print cloths, the number of threads on an 
inch are taken as the count, viz. If you have cloth woven 
in a 1200 reed, you multiply the count of the reed by 2, 
which will make 2400, and that divided by 36 will be 66, 
which will designate the count of that particular kind 
of goods. Throughout New England generally, the above 
count is used for all plain goods, and the number of dents 
in a reed for twilled. 

The first line in each division is the number of dents in 1 inch ; 
opposite to which is the count of the reed, according to the sys- 
tem of counting. 

JST.B.—A dent is generally called a split in Scotland ; a leer is 
generally called a porter in Scotland. 

Bleached or finished goods generally decrease in width about 
10 per cent. 



i 



REED TABLE. 



295 



REED TABLE. 



1 


2 


3 




4 




5 


United States. 


Bolton. 


Blackburn. 


6-4ths. 
Preston. 


9-8ths. 
Preston. 


N. of 


count 


N. of 


count 


N. of 


count 


N. of 


count 


N. of 


count 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. 


! in. 


reed. 


15 


30 


15 


18.187 


15 


33.75 


15 


43.5 


15 


33. 


16 


32 


16 


19.4 


16 


36. 


16 


46.4 


16 


35.2 


17 


34 


17 


20.612 


17 


38.25 


17 


49.3 


17 


37.4 


18 


36 


18 


21.825 


18 


40.5 


18 


52.2 


18 


39.6 


19 


38 


19 


23.037 


19 


42.75 


19 


55.1 


19 


41.8 


20 


40 


20 


24.25 


20 


45. 


20 


58. 


20 


44. 


21 


42 


21 


25.462 


21 


47.25 


21 


60.9 


21 


46.2 


22 


44 


22 


26.675 


22 


49.5 


22 


63.8 


22 


48.4 


23 


46 


23 


27.887 


23 


51.75 


23 


66.7 


23 


50.6 


24 


48 


24 


29.1 


24 


54. 


24 


69.6 


24 


52.8 


25 


50 


25 


30.31 


25 


56.25 


25 


72.5 


25 


55. 


26 


52 


26 


31.52 


26 


58.5 


26 


75.4 


26 


57.2 


27 


54 


27 


32.73 


27 


60.75 


27 


78.3 


27 


59.4 


28 


56 


28 


33.95 


28 


63. 


28 


81.2 


28 


61.6 


29 


58 


29 


35.16 


29 


65.25 


29 


84.1 


29 


63.8 


30 


60 


30 


36.87 


30 


67.5 


30 


87. 


30 


66. 


31 


62 


31 


37.58 


31 


69.75 


31 


89.9 


31 


68.2 


32 


64 


32 


38.8 


32 


72. 


32 


92.8 


32 


70.4 


33 


66 


33 


40.1 


33 


74.25 


33 


95.7 


33 


72 6 I 


34 


68 


34 


41.22 


34 


76.5 


34 


98.6 


34 


74.8 


35 


70 


35 


42.43 


35 


78.75 


35 


101.5 


35 


77. 


36 


72 


36 


43.65 


36 


81. 


36 


104.4 


36 


79.2 


37 


74 


37 


44.86 


37 


83.25 


37 


107.3 


37 


81.4 


38 


76 


38 
39 


46.07 


38 


85.5 


38 


110.2 


38 


83.6 


39 


78 


47.28 


39 


87.75 


39 


113.1 


39 


85.8 


40 


80 


40 


48.5 


40 


90. 


40 


116. 


40 


88. 


41 


82 


41 


49.71 


41 


92.25 


41 


118.9 


41 


90.2 


42 


84 


42 


50.9 


42 


94.5 


42 


121.8 


42 


92.4 


43 


86 


43 


52.13 


43 


96.75 


43 


124.7 


43 


94.6 


44 


88 


44 


53.35 


44 


99. 


44 


127.6 


44 


96.8 



296 



&EED TABLE. 



KEED TABLE. 



6 


7 


8 


9 


10 


n 


4-4ths. Preston. 


7-8ths. Preston. 


Nankeen. 


ScotGh. 


Silk. 




N. of 


count 


N.of 


count 


N.of 


count 


N.of 


count 


N.of 


count 


N. of 


Idts. in 
lin. 


of 


dts.in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


reed. 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. 


1 yard. 


15 


29.25 


15 


25.5 


15 


15.79 


15 


555 


15 


1080 


540 


16 


31.2 


16 


27.2 


16 


16.842 


16 


592 


16 


1152 


576 


17 


33.15 


17 


28.9 


17 


17.894 


17 


629 


17 


1224 


612 


18 


35.1 


18 


30.6 


18 


18.947 


18 


666 


18 


1296 


648 


19 


37.05 


19 


32.3 


19 


20. 


19 


703 


19 


1368 


684 


20 


39. 


20 


34. 


20 


21.052 


20 


740 


20 


1440 


720 


21 


40.95 


21 


35.7 


21 


22.105 


21 


777 


21 


1512 


756 


22 


42.9 


22 


37.4 


22 


23.157 


22 


814 


22 


1584 


792 


23 


44.85 


23 


39.1 


23 


24.21 


23 


851 


23 


1656 


828 


24 


46.8 


24 


40.8 


24 


25.26 


24 


888 


24 


1728 


864 


25 


48.75 


25 


42.5 


25 


26.31 


25 


925 


25 


1800 


900 


26 


50.7 


26 


44.2 


26 


27.36 


26 


962 


26 


1872 


936 


27 


52.65 


27 


45.9 


27 


28.42 


27 


299 


27 


1944 


972 


28 


54.6 


28 


47.6 


28 


29.47 


28 


1036 


28 


2016 


1008 


29 


56.55 


29 


49.3 


29 


30.52 


29 


1073 


29 


2088 


1044 


30 


58.5 


30 


51. 


30 


31.57 


30 


1110 


30 


2160 


1080 


31 


60.45 


31 


52.7 


31 


32.63 


31 


1147 


31 


2232 


1116 


32 


62.4 


32 


54.4 


32 


33.68 


32 


1184 


32 


2304 


1152 


33 


64.35 


33 


56.1 


33 


34.73 


33 


1221 


33 


2376 


1188 


34 


66.3 


34 


57.8 


34 


35.79 


34 


1258 


34 


2448 


1224 


35 


68.25 


35 


59.5 


35 


36.84 


35 


1295 


35 


2520 


1260 


36 


70.2 


36 


61.2 


36 


37.89 


36 


1332 


36 


2592 


1296 


37 


72.15 


37 


62.9 


37 


38.94 


37 


1369 


37 


2664 


1332 


38 


74.1 


38 


64.6 


38 


40. 


38 


1406 


38 


2736 


1368 


39 


76.05 


39 


66.3 


39 


41.05 


39 


1443 


39 


2808 


1404 


40 


78. 


40 


68. 


40 


42.1 


40 


1480 


40 


2880 


1440 


I 41 


79.95 


41 


69.7 


41 


43.15 


41 


1517 


41 


2952 


1476 


1 42 


81.9 


42 


71.4 


42 


44.21 


42 


1554 


42 


3024 


1512 


1 43 


83.85 


43 


73.1 


43 


45.26 


43 


1591 


43 


3096 


1548 


1 44 


85.8 


44 


74.8 


44 


46.31 


44 


1628 


44 


3168 


1584 



COUNTING REEDS. 297 

THE DIFFERENT SYSTEMS OF COUNTING REEDS. 

If there be 21 dents in an inch; what count of reed will it be 
in Manchester or Stockport? 

21 dents in an inch. 
2 ends in a dent. 

42 count of reed. 

If there be 26 dents in an inch, what count of reed will it be 
in Bolton, allowing 20 dents to a beer. 

24.25 inches. 

26 dents in an inch. 



14550 

4850 



Dents in a beer, 2.0)63.0.50 

31.525 count of reed. 

If there be 26 dents in an inch, what count of reed will it be 
in Bolton, allowing 19 dents to a beer ? 

24.25 inches. 

26 dents in an inch. 



14550 

4850 



Dents in a beer, 19)630.50(33.1842 count of reed. 

57 

60 
57 
- 80 

35 76 

19 
40 

160 38 

152 — 



20 



298 COUNTING REEDS. 

Suppose a reed contains 33 dents in 1 inch, what count will 
it be according to the different systems of counting? 

UNITED STATES, MANCHESTER, AND STOCKPORT. 

Multiply the number of dents in 1 inch by 2, and the product 
will be the count of the reed. 

33 number of dents in 1 inch. 
2 ends in a dent. 

66 count of reed. 

BOLTON COUNT, 20 DENTS TO A BEER. 

Multiply 24J by the number of dents in 1 inch, and divide hj 
20, and the quotient will be the count of the reed. 

24.25 inches. 

33 number of dents in 1 inch. 

7275 
7275 



Number of dents in a beer, 2.0)80.0.25 



40.0125 count of reed. 

BOLTON COUNT, 19 DENTS TO A BEER. 

Multiply 241 "by the number of dents in 1 inch, and divide by 
19, and the quotient will be the count of the reed. 

24.25 inches. 

33 dents in 1 inch. 





a beer, 


7275 
7275 


12 coi 




Dents in 


19)800.25(42. 
76 


int of reed 






40 

38 








« 


22 
19 


35 

38- 


-nearly. 



N.B. — Some hinds of goods manufactured in Bolton, reckon 19 
dents to a beer. 



REED TABLE. 



299 









REED TABLE. 










1 


2 




3 


4 


5 


United States. 


Bolton. 


Blackburn. 


6-4ths 
Preston. 


6-4ths 
Preston. 


N. of 


count 


N.of 


count 


N.of 


count 


N.of 


count 


N.of 


count 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


1 in. 
45 


reed. 


lin. 


reed. 


lin. 


reed. 


1 in. 


reed. 


lin. 


reed. 


90 


45 


54.56 


45 


101.25 


45 


130.5 


45 


99. 


46 


92 


46 


55.71 


46 


103.5 


46 


133.4 


46 


101.2 


47 


94 


47 


56.98 


47 


105.75 


47 


136.3 


47 


103.4 


48 


96 


48 


58.2 


48 


108. 


48 


139.2 


48 


105.6 


49 


98 


49 


59.41 


49 


110.25 


49 


142.1 


49 


107.8 


50 


100 


50 


60.62 


50 


112.5 


50 


145. 


50 


110. 


51 


102 


51 


61.83 


51 


114.75 


51 


148.9 


51 


112.2 


52 


104 


52 


63.04 


52 


117. 


52 


151.8 


52 


114.4 


53 


106 


53 


64.25 


53 


119.25 


53 


154.7 


53 


116.6 


54 


108 


54 


65.46 


54 


121.5 


54 


157.6 


54 


118.8 


55 


110 


55 


66.687 


55 


123.75 


55 


159.5 


55 


121. 


56 


112 


56 


67.9 


56 


126. 


56 


162.4 


56 


123.2 


57 


114 


57 


69.112 


57 


128.25 


57 


165.3 


57 


125.4 


58 


116 


58 


70.325 


58 


130.5 


58 


168.2 


58 


127.6 


59 


118 


59 


71.537 


59 


132.75 


59 


171.1 


59 


129.8 


60 


120 


60 


72.75 


60 


135. 


60 


174. 


60 


132. 


61 


122 


61 


73.962 


61 


137.25 


61 


176.9 


61 


134.2 


62 


124 


62 


75.175 


62 


139.5 


62 


179.8 


62 


136.4 


63 


126 


63 


76.387 


63 


141.75 


63 


182.7 


63 


138.6 


64 


128 


64 


77.6 


64 


144. 


64 


185.6 


64 


140.8 


65 


130 


65 


78.812 


65 


146.25 


65 


188.5 


65 


143. 


66 


132 


66 


80.025 


66 


148.5 


66 


191.4 


66 


145.2 


67 


134 


67 


81.237 


67 


150.75 


67 


194.3 


67 


147.4 


68 


136 


68 


82.45 


68 


153. 


68 


197.2 


68 


149.6 


69 


138 


69 


83.662 


69 


155.25 


69 


200.1 
203. 


69 


151.8 


70 


140 


70 


84.875 


70 


157.5 


70 


70 


154. 


71 


142 


71 


86.087 


71 


159.75 


71 


205.9 


71 


156.2 


72 


144 


72 


87.3 


72 


162. 


72 


208.8 


72 


158.4 


73 


146 73 


88.512 


73 


164.25 


73 


211.7 


73 


160.6 


74 


148 74 


89.725 


74 


166.5 


74 214.6 

1 1 


74 


162.8 



300 



REED TABLE. 



REED TABLE. 



6 


7 


8 


9 


10 


11 


4-4ths 
Preston. 


7-Sths 
Preston. 


Nankeen. 


Scotch. 


Silk. 




N.of 


count 


N.of 


count 


N. of j 


count 


N.of 


count | N. of 


count 


N. of 


dts. in 


of 


dts. in 


of 


dts. in 


of 


dts. in 


of idts. in 


of 


dts. in 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. 


1 in. 


reed. S 1 in. 


reed. 


1yd. 


45 


87.75 


45 


76.5 


45 


47.36 


45 


1665 1 45 


3240 


1620 


46 


89.7 


46 


78.2 


46 


48.42 


46 


1702 


46 


3312 


1656 


47 


91.65 


47 


79.9 


47 


49.47 


47 


1739 


47 


3384 


1692 


48 


93.6 


48 


81.6 


48 


50.52 


48 


1776 


48 


3456 


1728 


49 


95.55 


49 


83.3 


49 


51.57 


49 


1813 


49 


3528 


1764 


50 


97.5 


50 


85. 


50 


52.63 


50 


1850 


1 50 


3600 


1800 


51 


99.45 


51 


86.7 


51 


53.67 


51 


1887 


51 


3672 


1836 


52 


101.4 


52 
53 


88.4 


52 


54.72 


52 


1924 


52 


3744 


1872 


53 


103.35 


90.1 


53 


55.78 


53 


1961 


53 


3816 


1908 


54 


105.3 


54 


91.8 


54 


56.84 


54 


1998 


54 


3888 


1944 


55 


107.25 


55 


93.5 


55 


57.894 


55 


2035 


55 


3960 


1980 


1 56 


109.2 


56 


95.2 


56 


58.947 


56 


2072 


56 


4032 


2016 


I 57 


111.15 


57 


96.9 


57 


60. 


57 


2109 


57 


4104 


2052 


I 58 


113.1 


58 


98.6 


58 


61.052 


58 


2146 


58 
59 


4176 


2088 


1 59 


115.05 


59 


100.3 


59 


62.105 


59 


2183 


4248 


2124 


I 60 


117. 


60 


102. 


60 


63.158 


60 


2220 


60 


4320 


2160 


I 61 


118.95 


61 


103.7 


61 


64.21 


61 


2257 


61 


4392 


2196 


I 62 


120.9 


62 


105.4 


62 


65.263 


62 


2294 


62 


4464 


2232 


1 63 


122.85 


63 


107.1 


63 


66.316 


63 


2331 


63 


4536 


2268 


I 64 


124.8 


1 64 


108.8 


64 


67.368 


64 


2368 


64 


4608 


2304 


I 65 


126.75 


65 


110.5 


65 


68.421 


65 


2405 


65 


4680 


2340 


66 


128.7 


66 


112.2 


66 


69.473 


66 


2442 


66 


4752 


2376 


67 


130.65 


67 


113.9 


67 


70.526 


67 


2479 


67 


4824 


2412 


68 


132.6 


68 


115.6 


68 


71.579 


68 


2516 


68 


4896 


2448 


69 


134.55 


69 


117.3 


69 


72.631 


69 


2553 


69 


4968 


2484 


70 


136.5 


70 


119. 


70 


73.684 


70 


2590 


70 


5040 


2520 


71 


138.45 


71 


120.7 


71 


74.737 


71 


2627 


71 


5112 


2556 


72 


140.4 


72 


122.4 


72 


75.789 


72 


2664 


72 


5184 


2592 


73 


142.35 


73 


124.1 


73 


76.842 


73 


2701 


73 


5256 


2628 


74 


144.3 


74 


125.8 


74 


77.894 


74 


2738 


74 


5328 


2664 



COUNTING REEDS. 301 

BLACKBURN COUNT, 20 DENTS TO A BEER. 

Multiply 45 by the number of dents in an inch, and divide by 
the number of dents in a beer, and the quotient will be the count 
of the reed. 

45 inches. 

33 dents in an inch. 

135 

135 



Dents in a beer, 2.0)148.5 



74.25 count of reed. 

PRESTON 6-4ths COUNT, 20 DENTS TO A BEER. 

Multiply 58 by the number of dents in an inch, and divide by 
20, and the quotient will be the count of the reed. 

58 inches. 
33 dents in an inch. 



174 
174 



Dents in a beer, 2.0)191.4 

95.7 count of reed. 

PRESTON 9-8ths COUNT, 20 DENTS TO A BEER. 

44 inches. 

33 dents in an inch. 



132 

132 



Dents in a beer, 20)1452(72.6 
140 

52 
40 

120 

120 



302 COUNTING REEDS. 

N.B. — Some manufacturers in Oldham count same as Blach- 
hurn for fustians and velvets ; printing cloths are same as 
Manchester, 

PRESTON 4-4ths, OR YARD WIDE COUNT, 20 DENTS TO A BEER. 

Multiply 39 by the number of dents in an inch, and divide by 
the number of dents in a beer, and the quotient will be the count 
of the reed. 

39 inches. 

33 dents in an inch. 



117 
117 



Dents in a beer, 2.0)128.7 



64.35 count of reed. 

PRESTON 7-8ths COUNT, 20 DENTS TO A BEER. 

Multiply 34 by the number of dents in an inch, and divide by 
the number of dents in a beer, and the quotient will be the count 
of the reed. 

34 inches. 

33 dents in an inch. 

102 
102 

Dents in a beer, 2.0)112.2 



56.1 count of reed. 

NANKEEN COUNT, 19 DENTS TO A BEER. 

Multiply 20 by the number of dents in an inch, and divide by 
the number of dents in a beer, and the quotient will be the count 
of the reed. 

20 inches. 

33 dents in an inch. 

660 



COUNTING REEDS. 303 

Dents in a beer, 19)660(34.73, or nearly 34f, count of reed. 

57 



90 
76 

140 
133 

70 

57 

13 

SCOTCH AND CARLISLE COUNT. 

Multiply 37 by the number of dents in an inch, and the pro- 
duct will be the count of the reed. 

37 inches. 
33 dents in an inch. 



Ill 
111 



1221 count of reed. 



SILK COUNT. 



Multiply 36 by the number of dents in an inch, and that pro- 
duct by 2, which will be the count of the reed. 

36 inches. 
33 dents in an inch. 



108 
108 



1188 

2 ends in a dent. 



2376 count of reed. 



NUMBER OF DENTS IN A YARD. 



Multiply the number of dents in an inch by the number of 
inches in a yard, and the product will be the number of dents in 
a yard. 



304 COUNTING REEDS. 

33 dents in an inch, 
36 inches in a yard. 



198 



1188 dents in a yard. 

Some manufacturers count calicoes, checks, and handkerchiefs, 
by the number of beers in a yard, some 19, and some 20 dents 
to a beer. 

By 20 dents to a beer. 

36 inches 1 yard. 
33 dents in an inch. 



108 
108 



Dents in a beer, 2.0)118.8 



59.4 count of reed. 

By 19 dents to a beer. 

36 inches 1 yard. 
33 dents in an inch. 



108 

108 



Dents in a beer, 19)1188(62.526 count of reed. 
114 



48 
38 



100 
95 



— 120 
50 114 

38 

6 



COUNTING REEDS. 305 

Some manufacturers of fustians, velvets, velveteens, velveretts, 
satteens, &c, count by the number of beers set on 24 inches at 
the reed, some 20, and some 19 dents to a beer. 

24 inches. 

33 dents in an inch. 



72 
72 



Dents in a beer, 2.0)79.2 



39.6 count of reed. 

If there be 33 dents in an inch, how many beers, 19 dents to 
a beer, will there be in 24 inches? 

33 dents in an inch. 
24 inches. 

132 



Dents in a beer, 19)792(41.684 count of reed. 
76 



32 
19 



130 
114 



160 
152 



80 
76 



How many dents will there be in an inch, in a 6-4ths 145 
Preston reed? 

Multiply the count of the reed by the number of dents in a 



306 MANUFACTURING. 

beer, and divide by the number of inches any given number of 
beers is set on, and the quotient will be the number of dents in 
an inch. 

145 count of reed. 
20 dents to a beer. 



Inches set on, 58)2900(50, number of dents in an inch. 
290 





Whatever the count of the reed, or system of counting may 
be, by referring to the table, you. will find the number of dents 
in an inch. 

The number of dents in an inch multiplied by 2, and that 
product multiplied by the number of inches intended to be filled 
at the reed, will give the number of ends required in the warp, 
for any kind of plain goods. 



MANUFACTURING. 

Rules and examples for ascertaining the weight of warp and 
weft, required for the manufacture of any description of cotton 
goods, according to the length and width of the piece, and the 
fineness of yarns. 

On account of some kind of goods requiring to be laid a 
greater length on the warping mill than others, it will be found 
the most accurate to ascertain the length and weight of twist 
required for the warp, and divide by the number of cuts or pieces 
in the warp, which will give the length and weight of twist (ac- 
cording to its fineness) required for one cut, or piece of cloth. 

JSf. B. — The general allowance for waste, is about l-50th of the 
iveight of weft required to weave the piece. 

TO ASCERTAIN THE WEIGHT OF A WARP. 

RULE. — Multiply the length of the warp by the width in inches 
required at the reed, and that product by the number of ends in 



MANUFACTURING. 307 

an inch, for a dividend. Then multiply the number of yards in 
one hank by the number of hanks in the pound of twist for a 
divisor, and the quotient will be the weight of the warp. 

iV". B. — By referring to the reed table, the number of ends in an 
inch of any reed may be found, according to the system of 
counting. 

Required, the weight of number 36's twist, for a warp 146 
yards long, 29 inches wide at the reed, and 72 ends in an inch? 

146 yards, length of warp. 
29 inches, width at reed. 



1314 

292 



4234 

72 ends in an inch. 



8468 
29638 



Dividend, 304848 yards of twist in the warp. 

840 yards, 1 hank. 
36 hanks in 1 lb. 



5040 

2520 



Divisor, 30240 yards in 1 lb. of 36's twist. 

30240)304848(10 lbs., 1J oz. weight of warp. 
30240 



2448 

16 oz.=llb. 



14688 
2448 

39168 



308 MANUFACTURING. 

30240)39168(1 ounce. 
30240 



8928 

4 qrs., 1 oz. 



30240)35712(1 qr. 
30240 



5472 



The weight of warp or weft may be found in a much easier 
way, by dividing the number of yards of twist, or weft required, 
by the number of yards in 1 ounce, which will be found in the 
yarn table according to the fineness of the yarns, as in the follow- 
ing example: — 

Required, the weight of 36 's twist, for a warp 146 yards long, 
29 inches wide at the reed, and 72 ends in an inch ? 

146 yards, length of warp. 
29 inches, width of warp at reed. 



1314 

292 



4234 

72 ends in an inch. 



8468 
29638 

Dividend, 304848 yards in warp. 

Yards in 1 oz. of 36's twist, 1890)304848(161^ oz., or 10 lbs., 

1890 1J oz., wt. of warp. 



11584 
11340 



2448 

1890 

558 

4 qrs., 1 oz. 



MANUFACTURING. 309 

1890)2232(1 qr. 
1890 



342 



If there be 304848 yards of 36's twist, in a warp containing 
5 cuts or pieces; what weight of twist will there be in 1 piece? t 

Cuts, or pieces in warp, 5)304848 yards of twist in warp. 

Yds. in 1 oz. of 36's twist, 1890)60969.6(32 J oz., or 2 lbs., J oz., 

5670 wt. of twist required 

for 1 piece of cloth. 

4269 
3780 



489.6 

4 qrs., 1 oz. 



1890)1958.4(1 qr. 
1890 



• 68.4 

Required, the weight of number 36's weft, to weave a piece of 
cloth 30 yards long, 29 inches wide, and 84 threads, or picks in 
an inch, allowing l-40th for waste? 

30 yards, length of piece. 
29 inches, width of piece. 



870 
84 threads or picks in an inch. 

3480 

6960 



73080 
Allowance for waste, 1-40 1827 



Dividend, 74907 yards required to weave a piece. 



310 MANUFACTURING. 

Yards in 1 ounce, 1890)74907(39| oz., or 2 lbs., 7| oz., weight of 
5670 weft required to weave a piece 

of cloth. 

18207 
17010 



1197 

4 qrs., 1 oz. 



1890)4788(2 qrs. 
3780 



1008 



Or Thus, 
1 lea is 12.0 yds.)7490.7 yards of weft required to weave a piece. 

1 hank, 7 leas)624.225 



( 6)89.175 hanks, or 2 lbs., 7} oz., weight of 

Nos. of weft,36's< weft required. 

(6)14.8625 



2.477083 lbs. 

16 oz., 1 lb. 



2862500 

477083 



7.633333 oz. 

4 qrs., 1 oz. 



2.533333 qrs. 

Or Thus, 

840 yards, 1 hank, 
36 hanks, 1 lb. 



5040 
2520 

Divisor, 30240 yards in 1 lb. of 36's weft. 



MANUFACTURING. 311 

30240)74907(2 lbs. 7} oz., weight of weft required. 
60480 



14427 
16 

86562 
14427 



30240)230832(7| 
211680 



19152 



Required, the weight of number 60's twist, for a warp 146 
yards long, 39 inches wide, and 106 ends to an inch? 

146 yards, length of warp. 
39 inches, width at the reed. 



1314 

438 



5694 
106 ends in an inch. 



34164 
56940 



1 lea, 12.0 yards)60356.4 yards of twist in warp. 

1 hank is 7 leas)5029.7 leas of twist in warp. 

Numbers of twist 6.0)71.8.52857 hanks of twist in warp. 

11.9754761 lbs. of twist in warp. 
16 ounces, 1 lb. 



58528566 
9754761 



15.6076176 ounces. 

4 qrs., 1 oz. 



2.4304704 qrs. 



312 MANUFACTURING. 

The weight of twist required for the warp, is 11 lbs., 15 J oz. 

If there be 603564 yards of number 60's twist in a warp; 
what will it weigh ? 

Yards in 1 ounce of 60's twist, 3150)603564(1911 ounces, or 11 

3150 pounds, 15J oz., 
weight of warp. 

28856 
28350 



5064 
3150 



1914 

4 qrs., 1 oz. 

3150)7656(2 qrs. 
6300 



1356 



If a warp, 146 yards long, 39 inches wide, and 106 ends in an 
inch, weigh 12 lbs., what numbers of twist will it be ? 

146 yards, length of warp. 
39 inches, width of warp at reed. 

1314 

438 

5694 
106 ends in an inch. 

34164 

56940 



Wt» of warp 12 lbs.)603564 number of yards in a warp. 

5029T 



MANUFACTURING. 313 

1 hank is 840 yards)50297(59.87 nearly, number 60's twist. 
4200 



8297 
7560 



7370 
6720 

6500 

5880 

620 

What length and weight of number 80 's weft, will it require to 
weave a warp 146 yards long, 39 inches wide at the reed, and 
120 threads, or picks in an inch, allowing l-50th for waste ? 

146 yards, length of warp. 
120 threads, or picks in an inch. 



17520 

39 inches, width at reed. 



157680 
52560 



683280 
Add l-50th for waste 13665.6 



696945.6 yards required to weave the warp. 
1 lea is 12.0 yds.)69694.5.6 yds. of weft required to weave a piece. 
1 hank is 7 leas.)5807.88 leas of do. 



829.69714 hanks. 

7 leas, 1 hank. 



4.87998 leas. 

120 yards, 1 lea. 



21 



105.59760 yards. 



314 MANUFACTURINGS 

The length of weft required to weave the warp will be 829 
hanks, 4 leas, and 105f yards. 

Numbers of weft, 8.0)82.9.69714 hanks of 80's weft. 



10.371214 lbs. 

16 ounces, 


lib. 


2227284 
371214 




5.939424 oz. 

4 qrs., 1 


oz. 


3.757696 qrs. 





10 lbs. 5f oz., nearly 10 lbs., 6 oz. weight of 80's weft, required 
to weave the warp. 

What length and weight of number 60's twist, will it require 
for a piece of cloth 29J yards long, 39 inches wide, and 106 
ends in an inch ? 

29.2 yards, length of piece. 
39 inches, width at reed. 



2628 
876 



1138.8 

106 ends to an inch. 



68328 
113880 



Dividend, 120712.8 yards of twist required for a piece. 

840 yards, 1 hank. 
60's twist. 



Divisor, 50400 yards in 1 lb. of number 60's twist. 



MANUFACTURING. 315 

50400)120712.8(2 lbs., 6 J oz., weight of twist re- 
100800 quired for 1 piece of cloth. 

19912.8 

16 ounces, 1 lb. 



1194768 
199128 



50400)318604.8(6 ounces. 
302400 



16204.8 

4 qrs., 1 oz. 



50400)64819.2(1 qr. 
50400 



14419 



The weight of number 60 's twist required for 1 piece of cloth, 
is 2 lbs., 6J oz., or 11 lbs., 15J ounces, for 1 warp containing 
5 pieces. 

What weight of number 80's weft, will it require to weave 1 
piece of cloth 29J yards long, 120 picks, or threads in an inch, 
and 39 inches wide, allowing l-50th for waste ? 

840 yards 1 hank. 
80's weft. 



67200 divisor. 

29.2 yards, length of piece. 
120 picks, or threads in an inch. 



3504.0 



39 inches, width at reed. 



315360 
105120 



136656.0 
Add 1-fiOth for waste 273312 



318 MANUFACTURING. 

Yds. in 1 lb., 67200)139389.12(2 lbs., l-5th oz., weight of weft 
134400 required to weave a piece of cloth. 



4989.12 
16 

2993472 
498912 



67200)79825.92(1 ounce. 
67200 



12625 = l-5th. 

What number of ends will it require in a warp, to fill 50 inches 
in a 96 reed, Manchester count? 

96, count of reed. 
50 inches, width at reed. 



4800, number of ends required in warp. 

What number of ends will it require in a warp, to fill 40J 
inches in a 118 Manchester count ? 

118, count of Manchester reed. 
40.5 inches, width at reed. 



590 
4720 



4779.0 number of ends in warp. 

What number of ends will it require to fill 50 inches in a 60 
reed, Bolton count, 20 dents, or 40 ends to the beer ? 

60 reed, Bolton count. 
40 ends, or 20 dents in 1 beer. 



2400 

50 inches, width at reed. 



120000 



MANUFACTURING. 317 

24J inches, or 24.25)120000.00(4948 ends required in the warp. 
9700 



23000 

21825 

11750 

9700 



20500 
19400 

1100 

iV. B. — It is not requisite to carry out the decimal fractions of 
an end. 

For the different systems of counting reeds, see the reed table, 
with rules and examples. 

What number of ends will be required in a warp, to fill 51 
inches, in a 66 reed, Bolton count ? 

66 count of reed. 

40 ends, or 20 dents to a beer. 



2640 

51 inches, width at reed. 



2640 
13200 

134640 dividend. 

24J, or 24.25 inches.)134640(5552 ends required for warp. 
12125 



13390 
12125 

12650 
12125 



5250 

4850 

400 



318 MANUFACTURING. 

What number of ends will it require in a warp, to fill 30J 
inches in a 74 reed, Blackburn count ? 

74 count of reed. 
40 ends, or 20 dents to a beer. 

2960 
30.5 inches, width of warp at the reed. 



14800 
88800 



Beers seton45inches.)90280.0(2006 ends required for warp. 
90 



280 
270 

10 

What width will 2006 ends fill, in a 74 reed, Blackburn count ? 
74, count of reed. 
40 ends, or 20 dents to a beer. 



2960 divisor. 
Number of ends in warp, 2006 

45 inches, number of beers set on. 



10030 
8024 



90270 dividend. 

90270 dividend by 2960=30.5, or 30 J in. nearly, width of warp 
at reed. 

What number of ends will it require in a warp, to fill 49J 
inches, in a 135 reed, Blackburn count? 



MANUFACTURING. 319 

135, count of reed. 
40 ends, or 20 dents to a beer. 



5400 

49.5 inches, width of warp at the reed. 



27000 
48600 
21600 



f9)267300.0 

45 inches, or< 

( 5)29700 



5940 ends required in the warp. 

What number of inches will 5940 ends fill, in a 135 reed, 
Blackburn count ? 

135, count of reed. 

40 ends, or 20 dents to a beer. 



5400 divisor. 

5940 ends in the warp. 

45 inches, number of beers set on reed. 



29700 
23760 



5400)267300(49.5, or 49 j- inches, width of warp at 
21600 the reed. 



51300 
48600 

27000 
27000 



What number of ends must there be in a warp, to fill 48 inches 
in a Bolton 54 reed ; allowing only 19 dents, or 38 ends to a 
beer ? 



320 MANUFACTURING. 



54, count of reed. 

38 ends, or 19 dents to a beer. 

432 
162 

2052 
48 inches, width of warp at the reed. 



16416 

8208 



^o'ninches 3 ^ } 24.25)98496.00(4062 ends required in the warp, 
y ( \)\) 

14960 
14550 

4100 

4850 — nearly. 

What number of inches will 4062 ends fill in a Bolton 54 
reed ; allowing 19 dents, or 38 ends to a beer ? 

54, count of reed. 
38 ends, or 19 dents to a beer. 

432 
162 



2052 divisor. 

4062 ends in the warp. 
24.25 inches, numbers of beer set on. 



20310 
8124 

16248 

8124 



2052)98503.50(48 inches, width filled at the reed. 

8208 



16423 
16416 



MANUFACTURING. 321 

What number of ends must there be in a warp, to fill 39J 
inches in a Bolton 44 reed ; if there be 19 dents, or 38 ends to 
a beer ? 

44, count of reed. 

38 ends, or 19 dents to a beer. 



352 
132 



1672 

39.5, or 39J inches, width of 

warp at the reed. 

8360 

15048 

5016 



No. of beers set on 24.25 in.)66044.00(2723 ends required for 

4850 the warp. 



17544 

16975 



5690 
4850 

8400 

7275 

125 

What number of inches will 2724 ends fill in a 44 reed, Bolton 
count ; allowing 19 dents, or 38 ends to a beer? 

44, count of reed. 

38 ends, or 19 dents to a beer. 



352 
132 



1672 divisor. 



322 MANUFACTURING. 



2724 number of ends in the warp. 
24.25, or 24J inches, number of beers set on. 



13620 
5448 

10896 
5448 



1672)66057.00(39.5, or 39J inches, width filled at 
5016 the reed. 



15897 
15048 



8490 
8360 

130 

What number of ends must there be in a warp, to fill 51 j- 
inches, in a 6-4ths 110 reed, Preston count ? 

110, count of reed, 6-4ths Preston. 
40 ends, or 20 dents in a beer. 



4400 

51.5, or 51 J inches, width of warp 
at the reed. 



22000 
4400 
22000 



No. of beers set on 58in.)226600.0(3907, No. of ends required 

174 for the warp. 



526 

522 



400 

406 — nearly. 

What number of inches will 3907 ends fill, in a 6-4ths 110 
reed, Preston count ? 



MANUFACTURING. 323 

110 count of reed, 6-4ths Preston. 
40 ends, or 20 dents to a beer. 



4400 divisor. 

3907, number of ends in the warp. 
Number of beers set on 58 inches. 



31256 
19535 



4400)226606(51.5, or 51J inches, width filled 
22000 at the reed. 



6606 
4400 

22060 
22000 



60 

N. B. — The 6-4:ths Preston count of reeds, is the number of beers 
set on 58 inches, 20 dents, or 40 ends to a beer. 

The small difference which appears in the last two examples 
arises from the decimal of an end. 

What number of ends must there be in a warp, to fill 51J 
inches, in a 6-4ths 144 reed, Preston count ? 

144, number of beers set on 58 inches at the reed. 
40 ends, or 20 dents to a beer. 



5760 

51.5, or 51| inches, width of warp at the reed. 



28800 
5760 
28800 

296640.0 



324 MANUFACTURING. 

58 inches.)296640. 0(5114, number of ends required for the warp. 
290 



66 

58 

84 
58 

260 
232 

28 

What number of inches will 5114 ends fill, in a 6-4ths 144 



reed, Preston count ? 



144, count of reed. 

40 ends, or 20 dents to a beer. 



5760 divisor. 

5114, number of ends in the warp. 
Number of beers set on 58 inches. 



40912 
25570 



5760)296612(51.5, or 51J inches, filled at the 
28800 reed. 



8612 
5760 



28520 
28800— nearly. 

JV. B. — The divisor is ascertained by multiplying the number of 
beers set on any given number of inches {according to the 
adopted rule), by the number of ends in a beer at the reed; 
and the dividend by multiplying the number of ends in the 
warp, by the number of inches any given number of beers is 
set on at the reed. 



MANUFACTURING. 325 

What number of ends must there be in a warp to fill 40J 
inches, in a 9-8ths 125 reed, Preston count? 

125, count of reed. 

40 ends, or 20 dents to a beer. 



5000 

40.5, or 40 \ inches, width of warp at 
the reed. 



25000 
200000 



o. of beers set 1 44)202500.0(4602, number of ends required 
on inches, J %« \ ' fnr ,1, A*.™ 



265 
264 



100 

88 

12 

What number of inches will a warp containing 4602 ends fill, 
in a 9-8ths 125 reed, Preston count? 

125 count of reed. 

40 ends, or 20 dents in a beer. 



5000 divisor. 

4602 number of ends in the warp. 
Number of beers set on 44 inches. 



18408 
18408 



5.000)202.488 



40.4976, or nearly 40J inches, width the 
warp fills at reed. 

JV. B. — The 9-8ths Preston count of reeds is calculated according 
to the number of beers set on 44 inches, 20 dents to a beer. 



326 MANUFACTURING. 

When calculating the width at the reed any warp will fill ac- 
cording to the number 6*f ends, the count of the reed must be 
multiplied by the number of ends filling 1 beer at the reed, for 
a divisor, whether 2, 3, 4, or more ends be in a dent, which will 
be according to the kind of goods made. 

What number of ends must there be in a warp, to fill 39J 
inches, in a 9-8ths 105 reed, Preston count? 

105, count of reed. 
40 ends, or 20 dents to a beer. 



4200 

39.5, or 39J inches, width of warp 
at the reed. 



21000 
37800 
12600 



No. of beers set on 44 in.)165900. 0(3770 number of ends required 
132 for the warp. 



339 

308 



310 

308 

20 

What number of inches will a warp containing 3770 ends fill, 
In a 9-8ths 105 reed, Preston count? 

105, count of reed. 

40 ends, or 20 dents to a beer. 



4200 divisor. 

3770 number of ends in the warp, 
No. of beers set on 44 inches. 



15080 
15080 

165880 



MANUFACTURING. 327 

4200)165880(39.49, or 39J- inches, width filled at 
12600 the reed. 



39880 
37800 

20800 
16800 



40000 
37800 

2200 

N". B. — Some manufacturers in Preston count their 9-8tfAa, 
4:Aths, and *I-8ths reeds, in the same proportion to a 6Aths, 
set on 58 inches. 

What number of ends must there be in a warp, to fill 37 
inches in a 4-4th, or yard wide 115 reed, Preston count? 

115, count of reed. 

40 ends, or 20 dents to a beer. 



4600 

37 inches, width of warp at the reed. 



32200 
13800 

170200 



No. of beers set on 39 in.)170200(4364 number of ends required 

156 for the warp. 



142 
117 



250 
234 

160 
156 



4 

How many inches will a warp containing 4364 ends fill, in a 
4-4ths, or yard wide 115 reed, Preston count ? 



328 MANUFACTURING. 



115, count of reed. 

40 ends, or 20 dents to a beer. 



4600 divisor. 

4364 number of ends in the warp. 
Number of beers set on 39 inches. 



39276 
13092 



4600)170196(36.999, or 37 inches, width the warp 
13800 fills at reed. 



32196 

27600 

45960 
41400 

45600 
41400 

42000 
41400 

600 

N. B. — The kAths, or yard wide Preston count of reed, is calcu- 
lated according to the number of beers set on 39 inches, 20 
dents to a beer. 

What number of ends must there be in a warp, to fill 34J 
inches, in a 4-4ths, or yard wide reed, Preston count? 

96, count of reed. 
40 ends, or 20 dents to a beer. 



3840 

34.5, or 34 J inches width of warp at 
the reed. 



19200 
15360 
11520 

132480.0 



MANUFACTURING. 329 

No. of beers set on 39 in.)132480.0(3397, number of ends required 
117 for the warp. 

154 
117 

378 
351 



270 

273— nearly. 

How many inches will a warp containing 3397 ends fill, in a 
4-4ths or yard wide 96 reed, Preston count ? 

96, count of the reed. 
40 ends, or 20 dents to a beer. 



3840 divisor. 

3397 number of ends in the warp. 
No. of beers set on 39 inches. 



30573 
10191 



3840)132483(34.5, or 34| inches, warp fills 
11520 at the reed. 



17283 
15360 

19230 
19200 



30 

JV. B.— The 9-Sths set on 43 J inches ; the 4:Aths, or yard wide, 
set on 38f inches, and the 7-Sths set on 33 f inches, will be in 
proportion to the QAths reed being set on 58 inches, 

22 



330 MANUFACTURING. 

What number of ends must there be in a warp, to fill 32J 
inches, in a 7-8ths 66 reed, Preston count ? 

66, count of reed. 
40 ends, or 20 dents to a beer. 

2640 

32.5, or 32J inches, width of warp at 
- — - — the reed. 



13200 

5280 
7920 



No. of brs. set on 34 in.)85800.0(2523 number of ends required for 
68 the warp. 

178 
170 



80 
68 

120 
102 

18 

How many inches will a warp containing 2523 ends fill, in a 
7-8ths 66 reed, Preston count ? 

66, count of reed. 
40 ends, or 20 dents to a beer. 



2640 divisor. 

2523 number of ends in the warp. 
Number of beers set on 34 inches. 



10092 
7569 

85782 



MANUFACTUKING. 331 

2640)85782(32.49, or 32} inches, warp fills at the 
7920 reed. 



6582 
5280 

13020 
10560 

24600 
23760 

840 

JSf.B. — The 7-Sths Preston count of reeds is calculated by the 
number of beers set on 34 inches, 20 dents to a beer. 

What number of ends must there be in a nankeen warp, to 
fill 31} inches, in a 60 reed ? 

60, count of reed. 

38 ends, or 19 dents to a beer. 



480 
180 



2280 

31.5, or 31} inches, width of warp 
at the reed. 



11400 

2280 
6840 



No. of brs. set on, 2.0in.)7182,0.0 



3591 No. of ends required for the warp. 

What number of ends must there be in a nankeen warp, to fill 
21 inches, in a 48 reed ? 



332 MANUFACTURING. 



48, count of reed. 

38 ends, or 19 dents to a beer. 



384 
144 



1824 

21 inches, width of warp at the reed 

1824 

3648 



No. of beers set on 2.0 in.)3830.4 



1915 No. of ends required for the warp. 

What number of inches will a nankeen warp containing 1915 
ends fill, in a 48 reed? 

48, count of reed. 
38 ends in a beer. 



384 
144 



1824 divisor. 

1915, number of ends in the warp. 
20 inches, number of beers set on. 



1824)38300(21 inches, width warp fills at the reed. 
3648 



1820 
1824— nearly. 

ffl.B. — The nankeen count of reeds is calculated by the number 
of beers set on 20 inches, 19 dents to a beer. 

How many ends must there be in a warp, to fill 51 J- inches, 
in a 1850 reed, Scotch count? 



MANUFACTURING. 333 

1850, count of reed. 

51.5, or 51J inches, width of warp 

at the reed. 

9250 

1850 
9250 



952T5.0 

2 ends in a dent, or split. 



No of dents set on 37 in.)190550(5150 number of ends required 
185 for the warp. 

55 

37 

185 
185 



Now many inches will a warp containing 5150 ends fill, in a 
1850 reed, Scotch count ? 

1850, count of reed. 

2, number of ends in a dent, or split. 



3700 divisor. 

5150, number of ends in the warp. 
Number of dents set on 37 inches. 



36050 
15450 



3700)190550(51.5, or 51J inches, warp fills at 
18500 the reed. 



5550 
3700 

18500 
18500 



334 MANUFACTURING. 

N. B. — In Carlisle, Scotland, Ireland, and the United States of 
America, they calculate their reeds by the number of dents set 
on 37 inches. 
In Carlisle and Scotland a dent is generally termed a split. 

How many ends must there be in a warp, to fill 49 J inches, in 
a 2150 reed, Scotch count ? 

2150, count of reed. 

2, number of ends in a dent, 

or split. 

4300 

49.5, or 49J- inches, width of warp 
at the reed. 



21500 

38700 
17200 



No. of dents set on 37 in.)212850. 0(5752, number of ends re- 

185 quired for the warp. 



278 
259 



195 
185 

100 

74 

26 

How many inches will a warp containing 5752 ends fill, in a 
2150 reed, Scotch count? 

2150, count of reed. 

2, number of ends in a dent, or 

split. 

4300 divisor. 

5752, number of ends in the warp. 
Number of dents set on 37 inches. 



40264 

17256 

212824 



MANUFACTURING. 335 

4300)212824(49.49, or 49| inches, nearly, 
17200 warp fills at the reed. 

40824 
38700 



21240 

17200 

40400 

38700 



1700 

What number of ends must there be in a silk warp, to fill 19 
inches, in a 3700 reed ? 

3700, count of reed. 

19 inches, width of warp required 

at the reed. 

33300 
3700 



No. of ends in 36 in.)70300(1952 number of ends required 
36 for the warp. 



343 
324 



190 

180 

100 

72 



28 



How many inches will a silk warp containing 1952 ends fill, 
in a 3700 reed ? 

1952 number of ends in the warp. 
Number of ends in 36 inches. 



11712 

5856 

70272 



336 LINEN YARNS. 



Count of reed 3700)70272(18.99, or 19 inches, nearly, width 
3700 the warp fills at the reed. 



33272 
29600 

36720 
33300 

34200 
33300 

900 

JV. B.—The silk manufacturers generally calculate their reeds by 
twice the number of dents, or the number of ends in 36 inches 
at the reed. 



LINEN YARN TABLES. 

Showing the weight of 1 lea, or cut, English hank and bundle, 
Irish and Scotch hank, spangle, or spindle, and bundle, from 1 
to 300 leas or cuts in the pound progressively. 



The following are the different sizes of reels in use, with the 
different systems of making up yarns. 

YORKSHIRE REEL. 

3 yards, or 108 inches in circumference. 
100 threads, 1 lea, 30O yards. 
10 leas, 1 hank, 3.000 yards. 
20 hanks, 1 bundle, 60.000 yards. 
Sells per bundle. 

DORSET REEL. 

2J yards, or 81 inches in circumference, 
40 threads, 1 knot, 90 yards. 
20 knots, 1 ran, 1.800 yards. 
12 rans, 1 dozen, 21.600 yards. 
Sells per dozen. 

N. B.—This reel is not much in use, the Irish reel being gene- 
rally adopted. 



LINEN YARNS. 337 

IRISH AND SCOTCH REELS. 

2J yards, or 90 inches in circumference. 
120 threads, 1 cut, 300 yards. 
12 cuts, 1 hank, 3.600 yards. 
4 hanks, 1 spangle, 14.400 yards. 
12J- spangles, or 50 hanks, 1 bundle, 180.000 yds. 
Sells per spangle in bundles. 

POINTS IN WHICH THE THREE REELS AGREE. 

40 knots, or 2 rans, make 1 hank Irish and Scotch, 3.600 yards. 
8 hanks Dorset, or 4 hanks Irish and Scotch, make 1 spangle or 

spindle, 14.400 yards. 
1J- spangles or spindles, make 1 dozen Dorset, 21.600 yards. 
12J- spangles or spindles, or 50 hanks Irish and Scotch, or 3 

English bundles of 60.000 yards each, make 1 Irish bundle, 

180.000 yards. 

EXPLANATION TO THE LINEN YARN TABLES. 

The first column is the numbers of yarn, opposite to which is 
the weight according to the length weighed. 

i\T. B. — The pounds and ounces are avoirdupois weight, and the 
pennyweights and grains are troy weight. 

oz. dwts. grains, grains. 

14 11 16 or 7000 troy are equal to 1 lb. avoirdupois. 
18 5J or 437J troy are equal to 1 oz. avoirdupois. 

The following are the dividends according to the length weighed. 

Yards. Dividends. 

1 lea, or cut 300 7.000 

1 English hank 3.000 • 70.000 

1 Irish and Scotch hank 3.600 84.000 

1 spangle or spindle 14.400 336.000 

1 English bundle 60.000 1.400.000 

1 Irish bundle 180.000 4.200.000 

1 knot, Dorset 90 2.100 

1 ran, do. 1.800 42.000 

1 dozen, do. 21.600 504.000 

N. B. — By dividing any of the above dividends, according to the 
length weighed, by the number of grains in the weight, it will 
give the numbers of yarns ; or divide by the numbers of yams, 
and it will give the number of grains weight, according to the 
length weighed. 



338 



LINEN YAENS. 



LINEN YARN TABLE. 
From Number 1 to 110 leas or cuts in the pound. 



Weight per lea or cut of 


Weight per English hank 


Weight per English bun- 


300 yards. 


of 3000 yards. 


dle of 60,000 yards. 


Nos. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


1 


16 





0. 


10 








0. 


200 








0. 


2 


8 





0. 


5 








0. 


100 








0. 


3 


5 


6 


1.83 


3 


5 


6 


1.83 


66 


10 


12 


3.66 


4 


4 





0. 


2 


8 





0. 


50 








0. 


5 


3 


3 


15.5 


2 








0. 


40 








0. 


6 


2 


12 


3.66 




10 


12 


3.66 


33 


5 


6 


1.83 


7 


2 


5 


5. 




6 


15 


15. 


28 


9 


2 


14.5 


8 


2 





0. 




4 





0. 


25 








0. 


9 
10 




14 


4.27 




i 


14 


4.27 


22 


3 


10 


3.05 




10 


22.5 










0. 


20 








0. 


11 




8 


6.83 




14 


9 


22.63 


18 


2 


16 


13.72 


12 




6 


1.83 




13 


6 


1.83 


16 


10 


12 


3.66 


13 




4 


4.96 




12 


5 


14.61 


15 


6 


2 


19.3 


14 




2 


14.5 




11 


7 


19.5 


14 


4 


10 


10. 


15 




1 


5.16 




10 


12 


3.6 


13 


5 


6 


1.83 


16 







0. 




10 





0. 


12 


8 





0. 


17 




17 


3.76 




9 


7 


12.14 


11 


12 


4 


6.94 


18 




16 


4.88 




8 


16 


4.88 


11 


1 


14 


4.27 


19 




15 


8.41 




8 


7 


16.21 


10 


8 


7 


16.21 


20 




14 


14. 




8 





0. 


10 








0. 


25 




11 


16. 




6 


7 


7. 


8 








0. 


30 




9 


17.33 




5 


6 


1.83 


6 


10 


12 


3.66 


35 




8 


8. 




4 


10 


10. 


5 


11 


7 


19.5 


40 




7 


7. 




4 





0. 


5 








0. 


45 




6 


11 55 




3 


10 


3.05 


4 


7 


2 


0.61 


50 




5 


20. 




3 


3 


15.5 


4 








0. 


55 




5 


7.25 




2 


16 


13.72 


3 


10 


3 


7.54 


60 




4 


20.66 




2 


12 


3.66 


3 


5 


6 


1.83 


65 




4 


11.69 




2 


8 


9.92 


3 


1 


4 


4.96 


70 




4 


4. 




2 


5 


5. 


2 


13 


13 


0.5 


75 




3 


21.33 




2 


2 


10.33 


2 


10 


12 


3.66 


80 




3 


15.5 




2 





0. 


2 


8 





0. 


85 




3 


10.35 




1 


16 


2.02 


2 


5 


11 


19.08 


90 




3 


5.77 




1 


14 


4.27 


2 


3 


10 


3.05 


95 




3 


1.68 




1 


12 


11.3 


2 


1 


12 


11.34 


100 




2 


22. 




1 


10 


22.5 


2 








0. 


105 




2 


18.66 




1 


9 


13.1 


1 


14 


8 


6.33 


110 




2 


15.63 




1 


8 


6.8 


1 


13 


1 


15.77 



LINEN YARNS. 339 

Required, the weight of 1 lea of number 18's yarn? 

Dividend. 
Numbers of yarn, 18)7000(388.8 grains, or 16 dwts., 4f grains, 
54 weight required. 



160 
144 
160 

160 144 

144 

16 

Required, the weight of 1 English hank of number 18's yarn ? 

Dividend. 
Numbers of yarn, 18)70000(3888.88 grains, or 8 oz., 16 dwts., 
54 4| grains, weight required. 



160 




144 






160 


160 


144 


144 






160 


160 


144 


144 


16 



How many ounces, pennyweights, and grains, are there in 
3888.88 grains ? 

Grains. Grains. 
1 oz. is equal to 437.5)3888.88(8 ounces. 
35000 



1 pennyweight is 24 grs.)388.88(16 dwts. 

24 



148 
144 



4.88 grains. 
8 oz., 16 dwts., 4.88 grains, weight required. 



340 



LINEN YARNS, 



LINEN YARN TABLE. 
From Number 1 to 110 leas or cuts in 1 pound. 



Weight per Irish and 


Wei 


ght 


per spangle or 


Weight per 


Irish 


Scotch hank < 


)f 3600 yards. 


spindle c 


f 14,400 yards. 


bundle of 180,000 yards. 


Nos. 


lbs. 


oz. 


dvvts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


1 


12 








0. 


48 








0. 


600 








0. 


2 


6 








0. 


24 








0. 


300 








0. 


3 


4 








0. 


16 








0. 


200 








0. 


4 


3 








0. 


12 








0. 


150 








0. 


5 


2 


6 


7 


7. 


9 


9 


10 


22.5 


120 








0. 


6 


2 








0. 


8 


8 





0. 


100 








0. 


7 




11 


7 


19.5 


6 


13 


13 


0.5 


85 


11 


7 


19.5 


8 




8 





0. 


6 








0. 


75 








0. 


9 




5 


6 


1.83 


5 


5 


6 


1.83 


66 


10 


12 


3.6 


10 




3 


3 


15.5 


4 


12 


14 


14. 


60 








0. 


11 




1 


8 


6.86 


4 


5 


14 


21.95 


54 


8 


13 


6.1 


12 










0. 


4 








0. 


50 








0. 


13 




14 


14 


0.53 


3 


11 


1 


9.65 


46 


2 


8 


9.9 


14 




13 


13 


0. 5 


3 


6 


15 


15. 


42 


13 


13 


0.5 


15 




12 


14 


14. 


3 


3 


3 


15.5 


40 








0. 


16 




12 





0. 


3 








0. 


37 


8 





0. 


17 




11 


5 


8.67 


2 


13 


3 


5.2 


35 


4 


12 


20.8 


18 




10 


12 


3.66 


2 


10 


12 


3.66 


33 


5 


6 


1.8 


19 




10 


1 


22.05 


2 


8 


7 


16.21 


31 


9 


4 


19.1 


20 




9 


10 


22.5 


2 


6 


7 


7. 


30 








0. 


25 




7 


12 


9.5 


1 


14 


13 


3. 


24 








o- 


30 




6 


7 


7. 


1 


9 


10 


22.5 


20 








0. 


35 




5 


8 


20.5 


1 


5 


17 


4.5 


17 


2 


5 


5. 


40 




4 


14 


14. 


1 


3 


3 


15.5 


15 








0. 


45 




4 


4 


20.66 


1 


1 


1 


5.16 


13 


5 


6 


1.8 


50 




3 


15 


7.5 




15 


6 


13.5 


12 








0. ' 


55 




3 


8 


22.77 




13 


17 


13.59 


10 


14 


9 


22.6 


60 




3 


3 


15.5 




12 


14 


14. 


10 








0. 


65 




2 


17 


9.3 




11 


14 


20.73 


9 


3 


12 


14.8 


70 




2 


13 


13. 




10 


17 


17. 


8 


9 


2 


14.5 


75 




2 


10 


5. 




10 


4 


9. 


8 








0. 


80 




2 


7 


7. 




9 


10 


22.5 


7 


8 





0. 


85 




2 


4 


17.23 




9 





15.44 


7 





17 


3.7 


90 




2 


2 


10.33 




8 


9 


17.33 


6 


10 


12 


3.6 


95 




2 





9.21 




8 


1 


12.84 


6 


5 





23.0 


100 




1 


16 


18.5 




7 


12 


9.5 


6 








0. 


105 




1 


15 


2.5 




7 


5 


17.5 


5 


11 


7 


19.5 


110 




1 


13 


14.13 




6 


17 


21.54 




7 


4 


23.3 



LINEN YARNS. 341 

Required, the weight of 1 spangle of number 19's yarn ? 

Dividend. 
Numbers of yarn, 19)33600(17684.2 grains, weight required. 
19 

146 
133 



130 
114 



160 
152 



— 40 

80 38 

76 — 



How many pounds, ounces, and pennyweights are there in 
17684.2 grains ? . 

Grains. Grains. 
1 lb. is equal to 7000)17684.2(2 lbs., 8 oz., 7 dwts.,16i grains. 
14000 



1 oz. is equal to 437.5 grs.)3684.2(8 oz. 

35000 



1 dwt. is equal to 24 grs.)184.2(7 dwts. 

168 



16J grains. 

Required, the weight of 1 English bundle of number 34's yarn? 

Dividend. 
Numbers of yarn, 34)1400000(41176 grains, or 5 lbs., 14 oz., 2 
136 dwts., 3J grains. 





260 


40 


238 


34 






220 


60 


204 


34 






16 



342 



LINEN YARNS. 



LINEN YARN TABLE. 
From Number 115 to 300 leas in 1 pound. 



We 


ight per 


lea, or 


Weight per English 


w< 


iight p 


er Englis 


i bundle 


cut of 300 


yards. j hank of 3000 yards. 




of 60,000 yards. 


Nos. 


dwts. 


grains. |oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


115 


2 


12.86 


1 


7 


3.1 


1 


11 


15 


1.41 


120 


2 


10.33 




6 


1.8 


1 


10 


12 


3.66 


125 


2 


8. 


1 


5 


2.5 


1 


9 


10 


22.5 


130 


2 


5.84 


1 


4 


4.96 


1 


8 


11 


5.23 


135 


2 


3.85 


1 


3 


9.03 


1 


7 


12 


19.87 


140 


2 


2. 


1 


2 


14.5 


1 


6 


15 


14. 


145 


2 


0.27 


1 


1 


21.25 


1 


6 


1 


6.17 


150 


1 


22.66 


1 


1 


5.18 


1 


5 


6 


1.83 


155 


1 


21.16 


1 





14.11 


1 


4 


11 


18.25 


160 


1 


19.75 


1 





0. 


1 


4 





0. 


165 


1 


18.42 




17 


16.24 


1 


3 


7 


4.34 


170 


1 


17.17 




17 


3.74 


1 


2 


15 


0.29 


175 


1 


16. 




16 


16. 


1 


2 


5 


5. 


180 


1 


14.88 




16 


4.88 


1 


1 


14 


4.27 


185 


1 


13.83 




15 


18.37 


1 


1 


5 


10.06 


190 


1 


12.84 


15 


8.42 


1 





15 


8.42 


195 


1 


11.89 


14 


22.97 


1 





7 


11.48 


200 


1 


11. 


14 


14. 


1 








0. 


205 


1 


10.14 


14 


5.46 




15 


11 


2.76 


210 


1 


9.33 


13 


21.33 




15 


4 


8.16 


215 


1 


8.55 


13 


13.58 




14 


16 


2.62 


220 


1 


7.81 


13 


6.18 




14 


9 


22.63 


225 


1 


7.11 


12 


23.11 




14 


4 


1.22 


230 


1 


6.43 | 


12 


16.34 




13 


16 


15.45 


235 


1 


5.78 


12 


9.87 




13 


11 


5.95 


240 


1 


5.16 


12 


3.66 




13 


6 


1.83 


245 


1 


4.571 


11 


21.71 




13 


1 


2.785 


250 


1 


4. 


11 


16. 




12 


14 


14. 


255 


1 


3.45 


11 


10.5 




12 


10 


0.196 


260 


1 


2.923 


11 


5.23 




12 


5 


14.615 


265 


1 


2.414 


11 


0.14 




12 


1 


9.018 


270 


1 


1.925 


10 


19.25 




11 


15 


12.685 


275 
280 
285 


1 


1.454 


10 


14.54 




11 


11 


14. 


1 


1. 


10 


10. 




11 


7 


19. 


1 


0.561 


10 


5.67 




11 


4 


3. 


290 


1 


0.137 


10 


1.37 




11 





15. 


295 




23.728 


9 


21.28 




10 


15 


10. 


300 




23.333 


9 


17.33 




10 


12 


3. 



LINEN YARNS. 343 

Required, the weight of 1 Irish bundle of 66's yarn. 

Numbers of yarn, 66)4200000(63636.36 grains. 
396 



240 

198 



420 
396 

240 
198 



420 

396 



240 

198 

420 

396 

24 

Grains. Grains. 
1 lb. is equal to 7000)63636.36(9 lbs., 1 oz., 8 dwts., 6.86 grs. 
63000 weight required. 

1 oz. is equal to 437.5 grs.)636.36(l oz. 

4375 



8 dwt. is equal to 24 grns.)198.86(8 dwts. 

192 



grains, 



344 LINEN YARNS. 

Or, 

lbs. 
Numbers of yarn, 66)600(9 lbs., 1 oz., 8 dwts., 6.86 grains, 
594 weight required. 

6 
16 oz., 1 lb. 



Numbers of yarn, 66)96(1 oz. 



30 
437. 5 grains, 1 oz. 



Nos. of yarn, 66)13125.0(198.86 grains or 8 dwts., 6.86 grs. 

652 

594 

585 
528 

570 

528 

42 



LINEN YARNS. 



345 



LINEN YARN TABLE. 

From Number 115 to 300 leas, or cuts in 1 pound. 



Weight per Irish and 


Weight per spangle or 


Weight per Irish bundle of 


Scotch hank of 3600 yards. 


spindle of 14,400 yds. 


180,000 yards. 


Nos. 


oz. 


dwts. 


1 grains. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


115 


1 


12 


4.93 


6 


12 


8.74 


5 


3 


8 


17.23 


120 


1 


10 


22.5 


6 


7 


7. 


5 








0. 


125 


1 


9 


18.5 


6 


2 


15. 


4 


12 


14 


14. 


130 


1 


8 


16.65 


5 


16 


13.11 


4 


9 


15 


10.19 


135 


1 


7 


16.72 


5 


12 


13.38 


4 


7 


2 


0.61 


140 


1 


6 


18.5 


5 


8 


20.5 


4 


4 


10 


10. 


145 


1 


5 


21.81 


5 


5 


9.74 


4 


2 


3 


18.51 


150 


1 


5 


2.5 


5 


2 


4.5 


4 








0. 


155 


1 


4 


8.43 


4 


17 


9.74 


3 


13 


17 


1.37 


160 


1 


3 


15.5 


4 


14 


14. 


3 


12 





0. 


165 


1 


2 


23.59 


4 


11 


22.36 


3 


10 


3 


7.54 


170 


1 


2 


8.61 


4 


9 


10.47 


3 


8 


8 


13.87 


175 


1 


1 


18.5 


4 


7 


2. 


3 


6 


15 


15. 


180 


1 


1 


5.16 


4 


4 


20.66 


3 


5 


6 


1.83 


185 







16.55 


4 


2 


18.21 


3 


3 


16 


6.2 


190 







4.6 


4 





18.42 


3 


2 


9 


14.26 


195 




17 


22.76 


3 


17 


2.57 


3 


1 


4 


4.96 


200 




17 


12. 


3 


15 


7.5 


3 








0. 


205 




17 


1.756 


8 


13 


14.52 


2 


14 


15 


2.8 


210 




16 


16. 


3 


11 


23.5 


2 


13 


13 


0.5 


215 




16 


6.69 


3 


10 


10.29 


2 


12 


11 


20.88 


220 




15 


21.81 


3 


8 


22.77 


2 


11 


11 


14.41 


225 




15 


13.33 


3 


7 


12.84 


2 


10 


12 


3.66 


230 




15 


5.21 


3 


6 


4.37 


2 


9 


13 


11.36 


235 




14 


21.44 


3 


4 


21.28 


2 


8 


15 


12.34 


240 




14 


14. 


3 


3 


15.5 


2 


8 





0. 


245 




14 


. 6.857 


3 


2 


10.928 


2 


7 


3 


8.357 


250 




14 


0. 


3 


1 


7.5 


2 


6 


7 


7. 


255 




13 


17.411 


3 





5.147 


2 


5 


11 


19.088 


260 




13 


11.076 


2 


17 


9,307 


2 


4 


16 


19.846 


265 




13 


4.981 


2 


16 


8.924 


2 


4 


4 


3.054 


270 




12 


23.111 


2 


15 


9.444 


2 


3 


10 


3.055 


275 




12 


17.45 


2 


14 


10.81 


2 


2 


16 


17.72 


280 




12 


12. 


2 


13 


13. 


2 


2 


5 


5. 


285 




12 


6.73 


2 


12 


15.94 


2 


1 


12 


11.34 


290 




12 


1.65 


2 


11 


19.62 


2 


1 


1 


21.25 


295 




11 


20.74 


2 


10 


23.98 1 


2 





9 


21.28 


300 




11 


16. 


9 


10 


5. i-j 


2 








0. 



ya 



346 LINEN YARNS. 

Required, the weight of an Irish or Scotch hank of number 
68's yarn: — ■ 

Dividend. 
Numbers of yarn, 68)84000(1235.29 grains. 
68 



160 
136 



240 

204 



360 
340 

200 
136 



640 
612 

28 



Grains. Grains. 
1 oz. is equal to 437.5)1235.29(2 oz., 15 dwts., 0.29 grains, wt. 
8750 required. 



1 dwt. is equal to 24 grns.)360.29(15 dwts. 

24 



120 

120 



0.29 grain. 
How many yards are there in 1 lb. and in 1 oz. of number 68's 



yarn? 



300 yards is 1 lea, or cut. 
Numbers of yarn, 68 

20400 number of yards in 1 lb. 



LINEN YARNS. 347 



1 lb. is equal to 16 oz.)20400(1275 yards in 1 oz. 
16 



44 
32 

120 
112 

80 
80 

Required, the weight of 1 spangle of number 85's yarn : — 

Dividend. 
Numbers of yarn, 85)336000(3952.94 grains. 
255 

810 
765 

450 
425 



250 

170 



800 
765 

355 
340 

15 

Grains. Grains. 
1 oz* is equal to 437.5)3952.94(9 oz., dwts., 15.44 grs., weight 
39375 required. 



15.44 

If 1 spangle of linen yarn weighs 9 oz., 15 J grains; what 
numbers will it be ? 



348 LINEN YARNS, 

9 oz., 15.5 grains. 
437.5 grains are equal to 1 oz. 



3953.0 grains. 

Grains. Dividend. 
9 oz., 15J- grns. are equal to 3953)336000(85 leas, or cuts in 1 lb. 

31624 which is the nos. of yarn. 



19760 

19765 — nearly. 

How many yards of number 85's yarn are there in 1 lb. and 
in 1 oz. ? 

300 yards, 1 lea, or cut. 
85, numbers of yarn. 



(4)25500 yards in lib. 

16 oz., lib J 

( 4)6375 



1593.75, or 1593f yards in 1 oz. 
Required, the weight of an Irish, or Scotch hank of number 
95's yarn:— 

Dividend. 
Numbers of yarn, 95)84000(884.21 grains, weight required. 
760 

800 
760 

400 
380 

200 
190 

100 
95 



LINEN YARNS. 349 

Grains. Grains. 
1 oz. is equal to 437.5)884.21(2 oz., dwts., 9.91 grains, weight 
8750 required. 



9.21 grains. 

If 1 Irish or Scotch hank of linen yarn weighs 2 oz., dwts., 
9 J grains, what numbers will it be ? 

437.5 grains are equal to 1 oz. 
2 



875.0 grains are equal to 2 oz. 
Add 9.25 grains. 

884.25 grs. is equal to 2 oz., dwts., 9J grs. 

Grains. Dividend. 

884.25)84000.00(9499, or nearly 95 numbers of yarn. 

795825 



441750 
353700 



880500 

795825 

'846750 

795825 

50925 



350 LINEN YARNS. 

Required, the weight of 1 Irish bundle of number 107's yarn :— 

Dividend. 
Numbers of yarn, 107)4200000(39252.33 grains, weight required. 
321 

990 
963 

270 

214 



560 

535 



250 
214 

360 
321 



390 
321 

69 



Grains. Grains. 
1 lb. is equal to 7000)39252.33(5 lbs., 9 oz., 13 dwts., 283 
35000 grains, weight required. 

1 oz. is equal to 437.5 grns.)4252.33(9 oz. 

39375 



1 dwt. is equal to 24 grains)314.83(13 dwts. 

24 



74 
72 



2.83 grains. 

If 1 Irish bundle of linen yarn weighs 5 lbs., 9 oz., 13 dwts., 
2.83 grains, or 39252.33 grains, what number will it be? 



LINEN YARNS. 351 

Grains. 
39252.33)4200000.00(107, numbers of yarn. 
3925233 



27476700 
27476631 



69 

Required, the weight of 1 English bundle of number 138's yarn :— 

Dividend. 
Numbers of yarn, 138)1400000(10144.927 grs., weight required. 
138 



200 
138 

620 

552 



680 
552 

1280 
1242 

380 
276 

1040 

966 

74 

Grains. Grains. 
1 lb. is equal to 7000)10144.927(1 lb-, 7 oz., 3 dwts., 10.427 
7000 grains, weight required. 



1 oz. is equal to 437.5 grs.)3144.927(7 oz. 

30625 



1 dwt is equal to 24 grains)82.427(3 dwts« 

72 



10.427 grains. 



352 LINEN YARNS. 

If 1 English bundle of linen yarn weighs 1 lb., 7 oz., 3 dwts., 
10J grains, what numbers will it be ? 

Grains. Dividend. 
1 lb., 7 oz., 3 dwts., 10 J grs., =10145)1400000(138, numbers of 

10145 yarn nearly* 



38550 
30435 



81150 
81160— nearly. 

Bequired, the weight of 1 English hank of number 138's yarn : — 

Dividend. 

Numbers of yarn, 138)70000(507.246 grains, weight required. 
690 



1000 
966 



340 

276 

640 

552 



880 
828 

52 



Grains. Grains. 
1 oz. is equal to 437.5)507.246(1 oz., 2 dwts., 21} grns. nearly, 
4375 weight required. 



1 dwt. is equal to 24 grs.)69.746(2 dwts. 

48 



21.746 grains* 



LINEN YARNS. 353 

Required, the weight of 1 English bundle of number 128's 
yarn : — 

Dividend. 
Numbers of yarn, 128)1400000(10937.5 grains, weight required, 

128 



1200 
1152 



480 
384 

960 
826 

640 
640 

Grains. Grains. 
1 lb. is equal to 7000)10937.5(1 lb., 9 oz., weight required. 
7000 



1 oz. is equal to437.5 grs.)3937.5(9 oz. 

39375 

Required, the weight of 1 lea, or cut of 154's yarn: — 

Dividend. 
Numbers of yarn, 154)7000(45.45 grains, or nearly 1 dwt.,* 21 J- 
616 grains, weight required, 

840 
770 

700 
616 

840 

770 

70 



354 LINEN YARNS. 

Required, the weight of 1 English hank of number 154's 
yarn: — 

Numbers of yarn, 154)700000(454.54 grains, weight required. 
616 



840 
770 



700 
616 

840 

770 



700 
616 

84 



How many ounces, pennyweights, and grains, are there in 
454.54 grains? 

1 oz. is equal to 437.5 grns.)454.545454(1.03896 ounces. 

4375 437.5 grains =1 oz. 

17045 19480 

13125 27272 

11688 

39204 15584 

35000 



— 17.045000 grs., or 1 oz. 

42045 dwts., 17 grns., 

39375 weight required. 

26704 
26250 



454 



LINEN YARNS. 355 

Required, the weight of 1 English bundle of number 165's 
yarn : — 

Dividend. 
Numbers of yarn, 165)1400000(8484.848 grains, weight required. 
1320 



800 
660 



1400 
1320 

800 
660 

1400 
1320 

800 
660 



1400 
1320 

80 

How many pounds, ounces, pennyweights, and grains are there 
in 8484.848 grains ? 

Grains. Grains. 
1 lb. =7000)8484.848(1 lb., 3 oz., 7 dwts., 4.348 grains. 
7000 



1 oz. =437.5 grns.)1484.848(3 oz. 
13125 



1 dwt. =24 grains,)172.348(7 dwts. 
168 



4.348 grains. 

If 1 English bundle of yarn weighs 1 lb., 3 oz., 7 dwts., 4.348 
grains, or 1484.848 grains, what numbers will it be? 



356 LINEN YARNS. 

Dividend. 
1 bundle weighs 8484.848 grns.)1400000.000(165's nos. of yarn. 

8484848 



55151520 

50909088 

42424320 
42424240 



How many yards are there in 1 pound of 184's yarn ? 

184, numbers of yarn. 

300 yards are 1 lea of number 1. 



55200, number of yards in 1 lb. 

Required, the weight of 1 Irish or Scotch hank of number 

184's yarn : — 

Dividend. 
Numbers of yarn, 184)84000(456.52 grains, weight required. 
736 



1040 
920 



1200 
1104 



960 
920 

400 
368 

32 

Grains. Grains. 
1 oz. =437.5)456.52(1 oz., dwts., 19.02 grains, weight re- 
437.5 quired. 



19.02 grains. 



LINEN YARNS. 857 

Required, the weight of 1 English hank of number 180's 
yarn : — • 

Dividend. 
Numbers of yarn, 180)70000(388f grains, weight required. 
540 

1600 
1440 



1600 
1440 



160 



1 dwt. is equal to 24 grns.)388f (16 dwts., 4| grains, weight re- 

24 quired, 

148 
144 

4 8-9ths, 

Required, the weight of 1 Irish spangle, or Scotch spindle of 
number 196's: — 

Dividend. 
Numbers of yarn, 196)336000(1714.285 grains, weight required. 
196 

1400 
1372 

280 
196 

840 

784 

560 
392 
1120 

1680 980 



1568 



140 



358 LINEN YARNS. 

Grains. Grains. 
1 oz.=437.5)1714.285(3 oz., 16 d\fts., 17.785 grains, 
13125 weight required. 



1 dwt. = 24 grains,)401.785(16 dwts. 
24 



161 
144 



17.785 grains. 

How many yards are there in 1 oz. of number 196's ? 
196, numbers, or counts of yarn. 
300 yards are 1 lea of number l's. 

1 lb.«16 oz.)58800(3675 yards of nos. 196's in 1 oz. 

48 



108 
96 



120 
112 



80 
80 

Kequired, the weight of 1 lea, or cut of number 2l5 5 s weft: — 

Dividend. 
Numbers of yarn, 215)7000(32,558 grains, or 1 dwt., 8J grains, 
645 weight required. 

550 
430 

1200 
1075 

— 1750 

1250 1720 

1075 — - 

— 30 



LINEN YARNS. 359 

Required, the weight of 1 Irish or Scotch hank of number 
235's yarn:— 

Dividend. 
Numbers of yarn, 235)84000(357.446 grains, weight required, 

705 



1 dwt. = 24 grains, or 



1350 
1175 

1750 
1645 

1050 
940 

1100 
940 

1600 
1410 

190 

4)357.446 grains. 



6)89.3615 



14.89358, or 14 dwts., 21 J grs,, nearly, 

How many yards are there in 1 pound of number 235's yarn ? 

235, numbers of yarn. 

300 yards 1 lea, or cut of number l's< 

70500 number of yards required, 



360 LINEN YARNS. 

Required, the weight of 1 Irish bundle of number 130's yarn:-— 

Dividend. 
Numbers of yam, 130)4200000(32307.692 grs. weight required. 
390 



300 
260 



400 
390 

1000 
910 



900 

780 



1200 
1170 



300 
260 

40 

Grains. Grains. 
1 lb. =7000)32307.692(4 lbs., 9 oz., 15 dwts., 10 J- grains 
28000 nearly, weight required. 



1 02.^437.5 grns.)4307.692(9 oz. 
8937.5 



1 dwt. =24 grains,)370.192(15 dwts. 

24 

130 

120 



10.192 grains. 

If 1 Irish bundle of yarn weighs 4 lbs., 9 02., 15 dwts., 10.192 
grains, or 32307.692 grains, what numbers will it be ? 



LINEN YARNS. 361 

Dividend. 
Weight, 32307.692)4200000.00(130, numbers of yarn. 
32307692 



96923080 
96923076 



40 

Required, the weight of 1 English hank of number 245's 
yarn : — 

Dividend. 
Numbers of yarn, 245)70000(285.714 grains, weight required. 
490 



2100 

1960 

1400 
1225 

1750 
1715 



350 
245 

1050 

980 

70 

Grains. Grains. 
1 dwt. —24)285.714(11 dwts., 21f grains nearly, weight re- 
24 quired. 

45 

24 



21.714 



Required, the weight of 1 Irish or Scotch hank of number 
240's yarn: — 
24 



362 LINEN YAKNS. 

Dividend. 
Numbers of yarn, 240)84(i00(350 grains, weight required, 

720 



1200 
1200 



r 2)350 grains. 

1 dwt.=24 grns.< 

( 12)175 

14 dwts., 14 grs., weight required. 

How many yards are there in 1 Irish or Scotch hank of yarn ? 

300 yards, 1 lea, or cut. 
12 leas, or cuts, are 1 Irish or Scotch hank. 



3600 yards in 1 Irish or Scotch hank. 

Required, the weight of 1 Irish spangle or Scotch spindle of 
number 265's yarn :— 

Dividend. 
Numbers of yarn, 265)33600(1267.92 grains, weight required. 
265 



710 

530 

1800 
1590 

2100 

1855 

2450 
2385 

650 
530 

120 



LINEN YARNS. 



Grains. Grains. 
1 oz. =437.5)1267.92(2 oz., 16 dwts., 9 grains nearly, weight 
875.0 required. 



1 dwt. =24 grs.)392.92(16 dwts. 
24 



152 
144 



8.92 grains. 

How many yards are there in 1 oz. of number 265 ? s yarn? 

265 numbers of yarn. 
300 yards, 1 lea or cut. 



(4)79500 
1 lb. =16 ozJ ■ 

(4)19875 

4968.75, or 4968J yards in 1 oz. 

Required, the weight of 1 lea, or cut of number 298's yarn? 

Dividend. 
Numbers of yarn, 298)7000(23.49, or 23J grains nearly, weight 
596 required. 



1040 

894 



1460 
1192 



2680 
2682— nearly. 

Required, the weight of 1 English bundle of number 295's 
yarn : — 



364 LINEN YARNS* 

Dividend. 

Numbers of yarn, 295)70000(237.288 grains, weight required. 
590 



1100 

885 

2150 

2065 



850 
590 

2600 
2360 

2400 
2360 

40 

1 dwt. =24 grains)237. 288(9 dwts.,21J grains, weight required, 
216 



21.288 grains. 

How many yards are there in 1 lb. of number 295 's yarn ? 

295, numbers of yarn, 
300 yards in 1 lea or cut. 



88500 yards in 1 lb. of number 295's yarn. 

In calculating the weight of linen yarns required to produce 
any fabric of cloth, the rules are the same as those in cotton, 
with this exception only : 300 yards constitute the lea, or cut in 
linen, which counts in the numbers of yarn the same as 840 
yards in cotton. 

What will the weight of a linen warp be, 124 yards long, con- 
taining 2160 ends made from 80's yarn? 



LINEN YARNS. 365 

2160, ends in the warp. 
124 



8640 
4320 
2160 



Ilea =3.00 yards)2678.40 
Numbers of yarn, 8.0)89.2.8 



11.16 lbs. 

16 oz. are 1 lb. 



16 



2.56 oz. 

4 qrs., 1 oz. 



2.24 quarters. 
The weight of the warp will be 11 lbs., 2 oz., 2.24 qrs. 

If a warp be 34 inches wide at the reed, containing 2160 ends, 
how many ends will there be in the inch ? 

34)2160(63.53, or 63} ends in an inch at 
204 the reed. 



120 
102 



180 
170 

100 

102 — nearly. 

What weight of number 95's linen yarn will it require to weave 
a warp 124 yards long, 34 inches wide, and 76 picks, or threads 
in an inch? 



368 LINEN YARNS. 



124 yards, length of warp. 

34 inches, width of warp at the 
reed. 



496 

372 



4216 

76 picks, or threads in an inch. 



25296 
29512 



1 lea is equal to 3.00 yds.)3204.16 



Numbers of yarn, 95)1068.0533(11.2426 lbs. 

95 16 oz. are 1 lb. 



118 14556 

95 2426 



230 3.8816 

190 4 qrs. are 1 oz. 



405 3.5264, or 11 lbs., 3 oz., 
380 3-J qrs. neat weight 
required to weave 

253 the above. 

190 



633 
570 



63 
N. B. — Allowance must he made for waste. 

The length and weight of linen yarns required for manu- 
facturing any fabric of linen cloth, may be ascertained in the 
same manner as illustrated in the two preceding examples. 



WORSTED AND WOOLLEN YARNS. 367 



WORSTED AND WOOLLEN YARNS. 

All worsted and woollen yarns being sold by the gross, it is 
necessary that the manufacturer of worsted and woollen pieces 
be well acquainted with the weight per gross according to the 
fineness of the yarns, in order to insure the proper weight of the 
piece he is making. The yarn being too heavy, even if made 
from wool of a proper quality, gives an inferior appearance. 

It is particularly necessary for the spinner to keep a strict 
check upon the working of his machinery; wool being much 
sooner affected by the atmosphere than cotton. 

The usual plan of trying the fineness of worsted, or woollen 
yarns is, to weigh 1 hank, and if the result be doubtful, to take 
a quarter of a gross from each frame, or collectively, as circum- 
stances may require. 

The following tables will show the weight of 1 hank, 1 dozen, 
and 1 gross of worsted, or woollen yarns, from number 1 to 270 
hanks in the pound. 

If the weight of a less quantity than 1 hank should be re- 
quired, rules and examples will be found after the next table. 

EXPLANATION TO THE FOLLOWING TABLES. ■ 

The first and last columns contain the numbers or counts of 
yarn ; opposite to which in the table is the weight according to 
the length weighed. 

560 yards make 1 hank. 
12 hanks make 1 dozen. 
12 dozens, or 144 hanks make 1 gross. 

JV. B. — The pounds and ounces are avoirdupois weight ; the 
pennyweights and grains are troy weight. 

24 grains are equal to 1 pennyweight. 

18 pennyweights, 5 J grains troy are equal to 1 ounce avoirdupois. 

16 ounces are equal to 1 lb. 

Or, 

24 grains make 1 pennyweight. 
437J grains make 1 ounce avoirdupois. 
7000 grains make 1 pound avoirdupois. 



368 



WORSTED AND WOOLLEN YARNS. 



WORSTED AND WOOLLEN YARN TABLE. 

From Number 1 to 40 hanks in the pound. 





Weight o 


fl hank. 


Weight of 1 dozen. 


w 


sight of 1 


ajross. 




Nos. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


Jbs. 


oz. 


dwts. 


grains. 


Nos. 


1 


16 





0. 


12 








0. 


44 








0. 


1 


2 


8 





0. 


6 








0. 


72 








0. 


2 


3 


5 


6 


1.8 


4 








0. 


48 








0. 


3 


4 


4 





0. 


3 








0. 


36 








0. 


4 


5 


3 


3 


15.5 


2 


6 


7 


7. 


28 


12 


14 


14. 


5 


6 


2 


12 


3.6 


2 








0. 


24 








0. 


6 


7 


2 


5 


5. 




1! 


7 


19.5 


20 


9 


2 


14.5 


7 


8 


2 





0. 




8 





0. 


18 








0. 


8 


9 


1 


14 


4.2 




5 


6 


1.8 


16 








0. 


9 


10 


1 


10 


22.5 




3 


3 


15.5 


14 


6 


7 


7. 


10 


11 


1 


8 


6.8 




1 


8 


6.8 


13 


1 


8 


6. 


11 


12 


1 


6 


1.8 










0. 


12 








0. 


12 


13 


1 


4 


4.9 




14 


14 


0.5 


11 


1 


4 


4.9 


13 


14 
15 


1 


2 


14.5 




IS 


13 


0.5 


10 


4 


10 


10. 


14 


1 


1 


5.1 




12 


14 


14. 


9 


9 


10 


22.5 


15 


16 


I 





0. 




12 





0. 


9 








0. 


16 


17 




17 


3.7 




11 


5 


8.6 


8 


7 


9 


15.6 


17 


18 




16 


4.8 




10 


12 


3.6 


8 








0. 


18 


19 




15 


8.4 




10 


1 


22. 


7 


9 


4 


19.1 


19 


20 




14 


14. 




9 


10 


22.5 


7 


3 


3 


15.5 


20 


21 




13 


21.3 




9 


2 


14.5 


6 


13 


13 


0.5 


21 


22 




13 


6.1 




8 


13 


6.1 


6 


8 


13 


5.75 


22 


23 




12 


16.3 




8 


6 


8.1 


6 


4 


3 


4. 


23 


24 




12 


3.6 




8 





0. 


6 








0. 


24 


25 




11 


16. 




7 


12 


9.5 


5 


12 


2 


22. 


25 


26 




11 


5.2 




7 


7 


0.2 


5 


8 


11 


5.2 


26 


27 




10 


19.2 




7 


2 


0.6 


5 


5 


6 


1.8 


27 


28 




10 


10. 


] 


6 


15 


15. 


5 


2 


5 


5. 


28 


29 




10 


1.3 




6 


11 


7.5 


4 


15 


8 


4.1 


29 


30 




9 


17.3 




6 


7 


7. 


4 


12 


14 


14. 


30 


31 




9 


9.8 




6 


3 


12.6 


4 


10 


5 


21.1 


31 


32 




9 


2.7 




6 





0. 


4 


8 


0. 


0. 


32 


33 




8 


20.1 




5 


14 


21.9 


4 


5 


14 


21.6 


33 


34 




8 


13.8 




5 


11 


19. 


4 


3 


13 


22.5 


34 


35 




8 


7.9 




5 


8 


20.5 


4 


1 


15 


2.5 


35 


36 




8 


2.4 




5 


6 


1.8 


4 








0. 


36 


37 




7 


21.1 




5 


3 


10.7 


3 


14 


4 


22.2 


37 


38 




7 


16.2 




5 





23. 


3 


12 


11 


12.3 


38 


39 




7 


11.4 




4 


16 


19.8 


3 


11 


1 


14.45 


39 


40 




7 


7. 




4 


14 


14. 


3 


9 


10 


22.5 


40 



WORSTED AND WOOLLEN YARNS. 369 

If the weight of any shorter length than stated in the pre- 
ceding table should be required, it may be ascertained by taking 
the number opposite the length weighed as shown below for a 
dividend, and the numbers, or counts of yarn for a divisor, and 
the quotient will be the weight in grains; or, take the number of 
grains any given length weighs for a divisor, and the number 
opposite that given length for a dividend, and the quotient will 
be the numbers, or counts of yarn roving, &c. 





Given lengths. 






Yards. 


Dividends. 


1 gross, or 


80640 


1008000 


1 dozen, or 


6720 


84000 


1 hank, or 


560 


7000 


6 leas, or 


480 


6000 


5 leas, or 


400 


5000 


4 leas, or 


320 


4000 


3 leas,' or 


240 


3000 


2 leas, or 


160 


2000 


1 lea, or 


80 


1000 


f lea, or 


60 


750 


J lea, or 


40 


500 


\ lea, or 


20 


250 


J lea, or 


10 


125 


T ^ lea, or 


5 


62.5 


^o lea, or 


2 


25 


-so lea > or 


1 


12.5 



N.B. — The worsted reel is 2 yards in circumference, and 40 
threads round the reel make 1 lea, and 7 leas make 1 hank. 

Required the weight of 40 yards of a hank roving : — 

Look opposite 40 yards in the above table, and you will find 
500, which is the dividend, and divide by 4, the numbers, or 
counts of roving, and the quotient will be the weight in grains. 

Numbers, or counts of roving, 4 hanks)500 dividend. 



125 grains, or 5 penny- 
weights, 5 grains, 
weight required. 



370 



WORSTED AND WOOLLEN YARNS. 



WORSTED AND WOOLLEN YARN TABLE. 







From Number 41 to 80 hanks in the 


poun 


a. 




n 

Nos. 


Wght. 


of 1 hnk. 


Weight of 1 dozen. 


| Weight 


of 1 g 


ross. 


r 


dwts. 


grains. 


1 oz. 


dwts. 


grains. 


Jbs. 


oz. 


dwts. 


grains. 


jNos. 


41 


7 


2.7 


4 


12 


10.7 


3 


8 


3 


13.3 


41 


42 


6 


22.6 


4 


10 


10. 


3 


6 


15 


15. 


42 


43 


6 


18,7 


4 


8 


11.4 


3 


5 


10 


14.3 


43 


44 


6 


15. 


4 


6 


15.1 


i 3 


4 


6 


14.8 


44 


45 


6 


11.5 


1 4 


4 


20.6 


3 


3 


3 


15.5 


45 


46 


6 


8.1 


4 


3 


4. 


3 


2 


1 


14. 


46 


47 


6 


4.9 


4 


1 


13.2 


3 


1 





9.3 


47 


48 


6 


1.8 


4 





0. 


3 








0. 


48 


49 


5 


22.8 


3 


16 


17.7 


! 2 


15 





8.9 


49 


50 


5 


20. 


i 3 


15 


7.5 


2 


14 


1 


11. 


50 


51 


5 


17.2 


3 


13 


22.5 


2 


13 


3 


5.2 


51 


52 


5 


14.6 


3 


12 


14.8 


2 


12 


5 


14.6 


52 


53 


5 


12. 


3 


11 


8.4 


2 


11 


8 


14.3 


53 


54 


5 


9.6 


1 3 


10 


3. 


2 


10 


12 


15.6 


54 


55 


5 


7.2 


3 


8 


22.7 


2 


9 


16 


5.7 


55 


56 


5 


5. 


3 


7 


19.5 


2 


9 


2 


14.5 


56 


57 


5 


2.8 


3 


6 


17.1 


2 


8 


7 


16.2 


57 


58 
59 


5 


0.6 


! 3 


5 


15.7 


2 


7 


13 


4.8 


58 


4 


22.6 


3 


4 


15.2 


2 


7 





22.2 


59 


60 


4 


20.6 


3 


3 


15.5 ! 


2 


6 


7 


7. 


60 


61 


'4 


18.7 


3 


2 


16.5 


2 


5 


14 


0.1 


61 


62 


4 


16.9 


3 


1 


18.3 


2 


5 


2 


22.5 


62 


63 


4 


15.1 


3 





20.8 


2 


4 


10 


10. 


63 


64 


4 


13.3 


3 





0. 


2 


4 





0. 


64 


65 


4 


11.6 


2 


17 


9.3 


2 


3 


8 


3.2 


65 


66 


4 


10. 


2 


16 


13.7 


2 


2 


16 


13.7 


66 


67 


4 


8.4 


2 


15 


18.7 


2 


2 


17 


1.7 


67 


68 


4 


6.9 


2 


15 


0.3 


2 


1 


16 


2. 


66 


69 


4 


5.4 


2 


14 


6.4 


2 


1 


7 


3.2 


69 


70 


4 


4. 


2 


13 


13. 


2 





16 


16. 


70 


71 


4 


2.6 


2 


12 


20.1 


2 





8 


5.1 


71 


72 


4 


1.2 


2 


12 


3.6 


2 








0. 


72 


73 


3 


23.9 


2 


11 


11.6 




15 


10 


5.7 


73 


74 ! 


3 


22.6 


2 


10 


20.1 




15 


2 


11.1 


74 


75 


o 


21.3 


2 


10 


5. 




14 


13 


3. 


75 


76 


3 


20.1 


2 


9 


14.2 




14 


5 


18.1 


76 


77 1 


3 


18.9 


2 


8 


23.9 




13 


16 


19.4 


77 


78 | 


3 


17.7 


2 


8 


9.9 1 




13 


9 


19.5 


78 


79 | 


3 


16.6 


2 


7 


20.3 




13 


3 


0. 


79 


ll 


3 


15.5 


2 


7 


7. ' 




12 


14 


14. 


80 



WORSTED AND WOOLLEN YARNS. 871 

Required, the weight of 1 lea of number 36 's yarn: — 
Look opposite 1 lea, or 80 yards, and you will find 1000 which 
is the dividend, the numbers of yarn, i. e., 36's will be the divisor, 
and the quotient will be the weight in grains. 

Dividend. 
Numbers of yarn, 36's)1000(27.77 grains, or 1 dwt., 3f- grains, 
72 weight required. 



280 

252 

280 

252 



280 

252 

28 



If 1 lea, or 80 yards of yarn weigh 27.77 grains; what num- 
bers, or counts will it be? 

1000 is the dividend for 1 lea, or 80 yards. 
Weight of 1 lea, 27.77 grs.)1000.00(36, numbers, or counts of 

8333 yarn. 



1Q66Q 



Required, the weight of 1 hank of number 80's yarn:- 
7000 is the dividend for 1 hank, or 560 yards. 
Numbers of yarn, 8.0)700.0 



87.5 grains, or 3 dwts., 15J- grains weight 

required. 
If 1 hank, or 560 yards, weigh 3 dwts., 15J- grains, or 87.5 
grains; what numbers will it be? 

7000 is the dividend for 1 hank, or 560 yards. 
Weight of 1 hk. 87.5 grs.)7000.0(80, number of counts of yarn. 

7000 





N.B. — The above examples will be sufficient to illustrate the 
tables; but if more should be required, see cotton, the only 
difference being the length constituting the hank. 



372 



WORSTED AND WOOLLEN YARNS. 



WORSTED AND WOOLLEN YARNS. 

From Number 80 to 120 hanks in the pound. 



1 


Wgt. 


ofl hk. 


Weight of 1 dozen. 


Weight 


of 1 gross. 




Nos. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


Nos. 


81 


3 


14.4 


2 


6 


18. 




12 


8 


2.4 


81 


82 


3 


13.3 


2 


6 


5.4 




12 


1 


18.6 


82 


83 


3 


12.3 


2 


5 


17. 




11 


13 


20. 


83 


84 


3 


11.3 


2 


5 


5. 




11 


7 


20.5 


84 


85 


3 


10.3 


2 


4 


17.2 




11 


1 


22.3 


85 


86 


3 


9.4 


2 


4 


5.7 




10 


14 


9.9 


86 


87 


3 


8.4 


2 


3 


18.5 




10 


8 


19.2 


87 


88 


3 


7.5 


2 


3 


7.5 




10 


3 


7.5 


88 


89 


3 


6.6 


2 


2 


20.8 




9 


16 


4.3 


89 


90 


3 


5.7 


2 


2 


10.3 




9 


10 


22.5 


90 


91 


3 


4.9 


2 


2 


0. 




9 


5 


19.4 


91 


92 


3 


4. 


2 


1 


14. 




9 





19. 


92 


93 


3 


3.2 


2 


1 


4.2 




8 


14 


2.7 


93 


94 


3 


2.4 


2 





18.6 




8 


9 


7.4 


94 


95 


3 


1.6 


2 





9.2 




8 


4 


14.5 


95 


96 


3 


0.9 


2 





0. 




8 





0. 


96 


97 


3 


0.1 




17 


20.4 




7 


13 


17.2 


97 


98 


2 


23.4 




17 


11.6 




7 


9 


7.2 


98 


99 


2 


22.7 




17 


2.9 




7 


4 


23.3 


99 


100 


2 


22. 




16 


18.5 




7 





18. 


100 


101 


2 


21.3 




16 


10.1 




6 


14 


14.1 


101 


102 


2 


20.6 




16 


2. 




6 


10 


17.3 


102 


103 


2 


19.9 




15 


18. 




6 


6 


17.4 


103 


104 


2 


19.3 




15 


10.2 




6 


2 


19.3 


104 


105 


2 


J8.6 




15 


2.5 




5 


17 


4.5 


105 


106 


2 


18. 




14 


18.9 




5 


13 


9.9 


106 


107 


2 


17.4 




14 


11.5 




5 


9 


17. 


107 


108 


2 


16.8 




14 


4.2 




5 


6 


1.8 


108 


109 


2 


16.2 




13 


21.1 




5 


2 


12.2 


109 


110 


2 


15.6 




13 


14.1 




4 


17 


5.6 


110 


111 


2 


15. 




13 


7.2 




4 


13 


19. 


111 


112 


2 


14.5 




13 


0.5 1 


4 


10 


10. 


112 


113 


2 


13.9 




12 


17.8 1 1 


4 


7 


2.3 


113 


114 


2 


13.4 




12 


11.3 1 1 


4 


3 


20.1 


114 


115 


2 


12.8 




12 


4.9 I 1 


4 





15.2 


115 


116 


2 


12.3 




11 


22.6 




3 


15 


17.1 


116 


117 


2 


11.8 




11 


16.4 




3 


12 


14.8 


117 


118 


2 


11.3 




11 


10.3 




3 


9 


13.8 


118 


119 


2 


10.8 


A 


11 


4.3 




3 


6 


14. 


119 


120 


2 


10.3 


Li 


10 


22.5 




3 


3 


15.5 


120 



WORSTED AND WOOLLEN YARNS. 373 

Required, the length and weight of number 56's yarn, for a 
warp 128 yards long, 36 inches wide at the reed, and to have 
84 threads in an inch: — 

128 yards, length of warp. 
36 inches, width of warp at the reed. 



768 
384 



4608 

84, threads in an inch. 



18432 
36864 



387072, total No. of yds. of yarn in the warp. 



Yards. 
1 gross contains 80640 yds.)387072(4 gross. 

322560 



1 dozen contains 6720 yds.)64512(9 dozen. 

60480 



1 hank contains 560 yds.)4032(7 hanks. 

3920 



1 lea contains 80 yds.)112(l lea. 
80 



1 thread contains 2 yds.)32 

16 threads. 

The length of yarn required for the above warp will be 4 gross, 
9 dozen, 7 hanks, 1 lea, and 16 threads. 

560 yards, 1 hank. 
56, numbers of yarn. 



3360 

2800 



31360 number of yards in 1 lb. ? of 56's yarn. 



374 



WORSTED AND WOOLLEN YARNS. 



WORSTED AND WOOLLEN YARN TABLE. 

From Number 121 to 160 hanks in the pound. 



p 


Wght. 


of 1 hnk. 


Wei 


'ht of 1 dozen. 


Weight 


of 1 gross. 




Nos. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


Nos. 


121 


2 


9.8 


1 


10 


16.7 


1 


3 





18. 


121 
122 


122 


2 


9.3 


1 


10 


11. 


1 


2 


16 


3.3 


123 I 


2 


8.9 


1 


10 


5.4 


1 


2 


13 


8.1 


123 


124 


2 


8.4 


1 


9 


23.9 


1 


2 


10 


5.9 


124 


125 


2 


8. 


1 


9 


18.5 


1 


2 


7 


21. 


125 


126 


2 


7.5 


1 


9 


13.1 


1 


2 


5 


5. 


126 


127 


o 


7.1 


1 


9 


7.9 


1 


2 


2 


14. 


127 


128 


2 


6.6 


1 


9 


2.7 


1 


2 





0. 


128 


129 


2 


6.2 


1 


8 


21.6 


1 


1 


15 


16.4 


129 


130 


2 


5.8 


1 


8 


16.6 


1 


1 


13 


4.3 


130 


131 


2 


5.4 


1 


8 


11.7 


1 


1 


10 


17.1 


131 


132 


2 


5. 


1 


8 


6.8 


1 


1 


8 


6.8 


132 


133 


2 


4.6 


1 


8 


2. 


1 


1 


5 


20.7 


133 


134 


2 


4.2 


1 


7 


21.3 


1 


1 


3 


12.8 


1 134 


135 


2 


3.8 


1 


7 


16.7 


1 


1 


1 


5.1 


135 


136 


2 


3.4 


1 


7 


12.1 


1 





17 


3.7 


136 


137 


2 


3.1 


1 


7 


7.6 


1 





14 


21.6 


1 137 


138 


2 


2.7 


1 


7 


3.2 


1 





12 


16.3 


138 


139 


2 


2.3 


1 


6 


22.8 


1 





10 


11.8 


139 


140 


o 


2. 


1 


6 


18.5 


1 





8 


8. 


140 


141 


2 


1.6 


1 


6 


14.2 


1 





6 


4.9 


141 


142 


2 


1.3 


1 


6 


10. 


1 





4 


2.5 


142 


143 


2 


1. 


1 


6 


5.9 


1 





2 


0.9 


143 


144 


2 


0.6 


1 


6 


1.8 


1 








0. 


144 


145 


o 


0.2 


1 


5 


21.8 




15 


16 


5.2 


145 


146 


1 


23.9 


1 


5 


17.8 




15 


14 


5.6 


146 


147 


1 


23.6 


1 


5 


13.9 




15 


12 


6.6 


147 


148 


1 


23.3 


1 


5 


10. 




15 


10 


8.3 


148 


149 


1 


23. 


1 


5 


6.2 




15 


8 


10.6 


149 


150 


1 


22.6 


1 


5 


2.5 




15 


6 


13.5 


! 150 


151 


1 


22.3 


1 


4 


22.8 




15 


4 


16.9 


151 


152 


1 


22. 


1 


4 


19.1 




15 


2 


21. 


152 


153 


1 


21.7 


1 


4 


15.5 




15 


1 


1.7 


153 


154 


1 


21.4 


1 


4 


11.9 




14 


17 


12.4 


154 


155 


1 


21.1 


1 


4 


8.4 




14 


15 


18.3 


155 


156 


1 


20.8 


1 


4 


4.9 




14 


14 


0.5 


156 


157 


1 


20.5 


1 


4 


1.5 


14 


12 


7.3 


157 


158 


1 


20.3 


1 


3 


22.1 




14 


10 


14.7 


1 158 


159 


1 


20. 


1 


3 


18.8 




14 


8 


22.6 


| 159 


160 


1 


19.7 


1_ 


3 


15.5 




14 


7 


7. 


160 



WORSTED AND WOOLLEN YARNS, 375 

Yards. Yards in the warp. 
1 lb. of No. 56's =31360)387072(12.34 lbs., or 12 lbs., 5J oz. 

31360 16 oz., 1 lb. 



73472 204 
62720 34 



107520 5.44 oz. 
94080 4 qrs., 1 oz. 



1344001.76 qrs. 
125440-8960, remainder. 

The weight of yarn required for the above warp will be 12 
lbs., 5J oz. nearly. 

Required, the weight of number 66's yarn, to weave a warp 
128 yards long, 36 inches wide at the reed, and to have 88 picks, 
or threads in an inch : — 

128 yards, length of warp. 
36 inches, width of warp at the reed. 

768 

384 



4608 

88, number of picks, or threads in an inch, 



36864 
36864 



405504 No. of yds. of yarn required to weave 

the warp. 
Yards. Yards. 
1 gross contains 80640)405504(5 gross, 4 hanks, and 32 threads, 
403200 length of yarn required to 

— weave the warp. 

1 hank contains 560 yds.)2304(4 hanks. 

2240 



1 thread contains 2 yards,)64 

32 threads. 



376 WORSTED AND WOOLLEN YARNS. 

560 yards, 1 hank. 
66, numbers of yarn. 



3360 
3360 



36960, number of yards in 1 lb. of 66's yarn. 



WORSTED AND WOOLLEN YARNS, 



377 



WORSTED AND WOOLLEN YARN TABLE. 

From Number 161 to 200 hanks in the pound. 





Weight of 1 hank. 


Weight of 1 dozen. Weight of 1 


gross. 


| 1 


Nos. 


oz. 


dwt. 


grains. 


lbs. 


oz. 


dwts. 


grains. | lbs. 


oz. 


dwts. 


grains. 


| Nos. 


161 




1 


19.4 




1 


3 


12.2 


14 


5 


15.8 


1 161 


162 




1 


19.2 




1 


3 


9. 


14 


4 


1.2 


162 


163 




1 


18.9 




1 


3 


5.8 




14 


2 


11. 


163 


164 




1 


18.6 




1 


3 


2.7 




14 





21.3 


164 


165 




1 


18.4 




1 


2 


23.6 




13 


17 


13.6 


165 


166 




1 


18.1 




1 


2 


20.5 




18 


16 


0.7 


166 


167 




1 


17.9 




1 


2 


17.5 




13 


14 


12.4 


167 


168 




1 


17.6 




1 


2 


14.5 




13 


13 


0.5 


168 


169 




1 


17.4 




1 


2 


11.5 




IS 


11 


13. 


169 


170 




1 


17.1 




1 


2 


8.6 




13 


10 


1.9 


170 


171 




1 


16.9 


1 


2 


5.7 




13 


8 


15.2 


171 


172 




1 


16.7 




1 


2 


2.8 


13 


7 


4.9 


172 


173 




1 


16.4 




1 


2 


0. 


13 


5 


19. 


173 


174 




1 


16.2 




1 


1 


21.2 


13 


4 


9.6 


174 


175 




1 


16. 




1 


1 


18.5 


13 


3 


0.5 


175 


176 




1 


15.7 


1 


1 


15.7 


13 


1 


15.7 


176 


177 




1 


15.5 




1 


1 


13. 


13 





7.4 


177 


178 




1 


15.3 




1 


1 


10.4 




12 


17 


4.9 


178 


179 




1 


15.1 




1 


1 


7.7 




12 


15 


21.2 


179 


180 




1 


14.8 




1 


1 


5.1 




12 


14 


14. 


180 


181 




1 


14.6 




1 


1 


2.5 




12 


13 


7. 


181 


182 




1 


14.5 


1 


1 


0. 




12 


12 


0.4 


182 


183 




1 


14.2 


1 





21.5 




12 


10 


18.1 


183 


184 




1 


14. 


1 





19. 




12 


9 


12.2 


184 


185 




1 


13.8 


1 





16.5 




12 


8 


6.6 


185 


186 




1 


13.6 


1 





14.1 




12 


7 


1.3 


186 


187 




1 


13.4 


1 





11.7 




12 


5 


20.3 


187 


188 




1 


13.2 




1 





9.3 | 


12 


4 


15.7 


188 


189 




1 


13. 




1 





6.9 




12 


3 


11.3 


189 


190 




1 


12.8 




1 





4.6 




12 


2 


7.2 


190 


191 




1 


12.6 




I 





2.3 




12 


1 


3.4 


191 


192 




1 


12.4 




1 





0. 




12 





0. 


192 


193 




1 


12.2 






18 


3.2 




11 


17 


2.3 


193 


194 




1 


12. 






18 


0.9 




11 


15 


23.3 


194 


195 




1 


11.8 






17 


22.7 




11 


14 


20.7 


195 


196 




1 


11.7 






17 


20.5 




11 


13 


18.3 


196 


197 




1 


11.5 






17 


18.4 




11 


12 


16.2 


197 


198 




1 


11.3 






17 


16.2 




11 


11 


14.4 


198 


199 




1 


11.1 






17 


14.1 




11 


10 


12.8 


199 


200 




1 


11. 






17 


12. 




11 


9 


11.5 


200 



25 



378 WORSTED AND WOOLLEN YARNS. 

Yards. Yards in the warp. 
1 lb. of No. 66 ? s = 36960)405504(10 lbs., 15$ oz., wt. of weft re- 

36960 quired to weave the warp. 

35904 

16 oz. 1 lb. 



215424 
35904 



36960)574464(15 oz. 
36960 



204864 

184800 



20064 

4 qrs., 1 oz. 



36960)80256(2 qrs. 
73920 



6336 



If it requires 12 lbs., 5J oz. of yarn for a warp, and 10 lbs. ? 
15.J qz. of yarn to we-ave the w^ r P \ what weight will it require 
for 1" piece, if there be 4 pieces in the warp? 

lbs. oz 

12 

10 

No. of pieces in warp, 4)23 



lbs. oz. 

12 . . 5 J, weight of the warp. 

10 . . 15J, weight to weave the warp. 

5 

13J, weight of 1 piece. 



N. B. — The rules, examples, and illustrations laid down for the 
manufacture of cotton goods, may be applied to the manufac- 
ture of any other fabric of cloth, such as linen, worsted, woollen, 
or silk; the system of calculation being the same, with the ex- 
ception of the length constituting the lea and hank, all particu- 
lars of which will be found in their proper places in this book. 



WORSTED AND WOOLLEN YARNS. 



379 



WORSTED AND WOOLLEN YARN TABLE. 

From Number 201 to 270 hanks in the pound. 





Wgt. of 1 hank. 


Weight of 1 dozen. 


Weight 


of 1 gross. 




Nos. 


dwts. 


grains. 


oz. 


dwts. 


grains. 


lbs. 


oz. 


dwts. 


grains. 


Nos. 


201 


1 


10.8 




17 


9.9 




11 


8 


10.4 


201 


202 


1 


10.6 




17 


7.8 




11 


7 


9.6 


202 


203 


1 


10.4 




17 


5.8 




11 


6 


9. 


203 


204 


1 


10.3 




17 


3.7 




11 


5 


8.6 


204 


205 


1 


10.1 




17 


1.7 




11 


4 


8.5 


205 


206 


1 


9.9 




16 


23.7 




11 


3 


8.7 


206 


207 


1 


9.8 




16 


21.8 




11 


2 


9. 


207 


208 


1 


9.6 




16 


19.8 




11 


1 


9.6 


208 


209 


1 


9.4 




16 


17.9 




11 





10.4 


209 


210 


1 


9.3 




16 


16. 




10 


17 


17. 


210 


211 


1 


9.1 




16 


14.1 




10 


16 


18.2 


211 


212 


1 


9. 




16 


12.2 




10 


15 


19.7 


212 


213 


1 


8.8 




16 


10.3 




10 


14 


21.3 


213 


214 


1 


8.7 




16 


8.5 




10 


13 


23.2 


214 


215 


1 


8.5 




16 


6.7 




10 


13 


1.3 


215 


216 


1 


8.4 




16 


4.8 




10 


12 


3.6 


216 


217 


1 


8.2 




16 


3.1 




10 


11 


6.1 


217 


218 


1 


8.1 




16 


1.3 




10 


10 


8.8 


218 


219 


1 


7.9 




15 


23.5 




10 


9 


11.7 


219 


220 


1 


7.8 




15 


21.8 




10 


8 


14.8 


220 


221 


1 ! 


7.6 




15 


20.1 




10 


7 


18. 


221 


222 


1 


7.5 




15 


18.3 




10 


6 


21.5 


222 


223 


1 


7.3 




15 


16.6 




10 


6 


1.1 


223 


224 


1 


7.2 




15 


15. 




10 


5 


5. 


224 


225 


1 


7.1 




15 


13.3 




10 


4 


9. 


225 


226 


1 


6.9 




15 


11.6 




10 


3 


13.1 


226 


227 


1 


6.8 




15 


10. 




10 


2 


17.5 


227 


228 


1 


6.7 




15 


8.4 




10 


1 


22. 


228 


229 


1 


6.5 




15 


6.8 




10 


1 


2.7 


229 


230 


1 


6.4 




15 


5.2 




10 





7.6 


230 


231 


1 


6.3 




15 


3.6 




9 


17 


18.1 


231 


232 


1 


6.1 




15 


2. 




9 


16 


23.3 


232 


235 


1 


5.7 




14 


21.4 




9 


14 


15.8 


235 


240 


1 


5.1 




14 


14. 




9 


10 


22.5 


240 


245 


1 


4.5 




14 


6.8 




9 


7 


8.7 


245 


250 


1 


4. 




14 


0. 




9 


3 


22.5 


250 


255 


1 


3.4 




13 


17.4 




9 





15.4 


255 


260 


1 


2.9 




13 


11. 




8 


15 


16.9 


260 


265 


1 


2.4 




13 


5. 




8 


12 


15.7 


265 


270 


1 


1.9 




12 


23.1 




8 


9 


17.3 


270 



380 WORSTED REEDS. 



WORSTED COUNT OF REEDS. 

The following are the general acknowledged methods of 
counting and expressing reeds in the manufacturing of all 
worsted goods. 

1st. The plain back, or three ends in a dent, the counts, or 
fineness of the set, which is expressed by the number of scores, 
or beers, 20 dents to a beer set on 6-4ths, or 54 inches at the 
reed. Thus, a 42 contains 42 scores, or 42 beers, 20 dents to a 
beer, or 840 dents on 54 inches at the reed. 

iV". B. — This reed is the most common one in use at the present 
time. 

2d. The wildbore, or 4 ends in a dent, the count, or fineness 
of the set, which is expressed by the number of scores, or beers, 
20 dents to a beer, set on 8-4ths, or 72 inches at the reed. 
Thus, a 50 wildbore slaie, or reed, contains 50 scores, or 50 
beers, 20 dents to a beer, or 1000 dents on 72 inches at the reed. 

N. B.— This method is very little in use now. 

3d. The 2 ends in a dent is coming more into use, the fineness 
of the set, which is expressed by the number of scores, or beers, 
20 dents to a beer set on 4-4ths or 36 inches at the reed. 

4th. Lastings. The count, or fineness of the set, which is ex- 
pressed by the number of dents set on 30 inches at the reed. 
Thus a 4 contains 400 dents, a 4J contains 450 dents, &c. &c. 

The following tables will show the count, or fineness of worsted 
reeds, according to the number of dents in an inch, and the 
different systems of counting. 

EXPLANATION TO THE REED TABLES. 

The first line in each division contains the number of dents in 
an inch ; opposite to which in the table is the count of the reed ? 
according to the different systems of counting. 

JV. B. — The decimal in the line expressing the number of dents 
in an inch, is the decimal of a dent. Thus, 20.5 is equal to 
20J dents, and the decimal in the lines expressing the counts 
of the reeds, is the decimal of a score, or beer containing 20 
dents. Thus, 40.5 is equal to 40| scores, or beers. 



WORSTED REEDS. 



381 



WORSTED REED TABLE. 



g . 
m O 
H.S 

V 


Scores, or 
beers on 
54 inches. 


Scores, or 
beers on 
72 inches. 


Scores, or j 
beers on 
36 inches. 1 


a m 
o v 

So 

C G 

m — * 


.2 • 

in y 
C.S 
v _ 


Scores, or 1 
beers on 
54 inches. 1 


Scores, or | 
beers on 
72 inches. 1 


Scores, or | 
beers on 
36 inches, f 


.5 S 1 

<u •— 

M co 


8. 


21.6 


28.8 


14.4 


240 


25.5 


68.85 


91.8 


45.9 


765 


8.5 


22.95 


30.6 


15.3 


255 


26. 


70.2 


93.6 


46.8 


780 


9. 


24.3 


32.4 


16.2 


270 126.5 


71.55 


95.4 


47.7 


795 


9.5 


25.65 


34.2 


17.1 


285 


27. 


72.9 


97.2 


48.6 


810 


10. 


27. 


36. 


18. 


300 


27.5 


74.25 


99. 


49.5 


825 


10.5 


28.35 


37.8 


18.9 


315 


28. 


75.6 


100.8 


50.4 


840! 


11. 


29.7 


39.6 


19.8 


330 


28.5 


76.95 


102.6 


51.3 


855 


11.5 


31.05 


41.4 


20.7 


345 


29. 


78.3 


104.4 


52.2 


870 


12. 


32.4 


43.2 


21.6 


360 


29.5 


79.65 


106.2 


53.1 


885 


12.5 


33.75 


45. 


22.5 


375 


30. 


81. 


108. 


54. 


900 


13. 


35.1 


46.8 


23.4 


390 


30.5 


82.35 


109.8 


54.9 


915 


13.5 


36.45 


48.6 


24.3 


405 


31. 


83.7 


111.6 


: 55.8 


930 


14. 


37.8 


50.4 


25.2 


420 


31.5 


85.05 


113.4 


56.7 


945 


14.5 


39.15 


52.2 


26.1 


435 


32. 


86.4 


115.2 


57.6 


960 


15. 


40.5 


54. 


27. 


450 


32.5 


87.75 


117. 


58.5 


975 


15.5 


41.85 


55.8 


27.9 


465 


33. 


89.1 


118.8 


59.4 


990 


16. 


43.2 


57.6 


28.8 


480 


33.5 


90.45 


120.6 


60.3 


1005 


16.5 


44.55 


59.4 


29.7 


495 


34. 


91.8 


122.4 


61.2 


1020 


17. 


45.9 


61.2 


30.6 


510 


34.5 


93.15 


124.2 


62.1 


1035 


17.5 


47.25 


63. 


31.5 


525 


35. 


94.5 


126. 


63. 


1050 


18. 


48.6 


64.8 


32.4 


540 


•35.5 


95.85 


127.8 


63.9 


1065 


18.5 


49.95 


66.6 


33.3 


555 


36. 


97.2 


129.6 


64.8 


1080 


19. 


51.3 


68.4 


34.2 


570 


36.5 


98.55 


131.4 


65.7 


1095 


19.5 


52.65 


70.2 


35.1 


585 


37. 


99.9 


133.2 


66.6 


1110 


20. 


54. 


72. 


36. 


600 


37.5 


101.25 


135. 


67.5 


1125 


20.5 


55.35 


73.8 


36.9 


615 


38. 


102.6 


136.8 


68.4 


1140 


21. 


56.7 


75.6 


37.8 


630 38.5 


103.95 


138.6 


69.3 


1155 


21.5 


58.05 


77.4 


38.7 


645 1 
660 


39. 


105.3 


140.4 


70.2 


1170 


22. 


59.4 


79.2 


39.6 


39.5 


106.65 


142.2 


71.1 


1185 


22.5 


60.75 


81. 


40.5 


675 


40. 


108. 


144. 


72. 


1200 


23. 


62.1 


82.8 


41.4 


690 


40.5 


109.35 


145.8 


72.9 


1215 


23.5 


63.45 


84.6 


42.3 


705 


41. 


110.7 


147.6 


73.8 


1230 


24. 


64.8 


86.4 


43.2 


720 


41.5 


112.05 


149.4 


74.7 


1245 


24.5 


66.15 


88.2 


44.1 


735 1 42. 


113.4 


151.2 


75.6 


1260 


25. 


67.5 


90. 


45. 


750 1 42.5 


114.75 


153. 


76.5 


1275 



382 WORSTED REEDS. 

To ascertain the count, or fineness of worsted reeds. 

RULE. — Multiply the number of dents in an inch by the 
given number of inches any reed is set on, according to the sys- 
tem of counting, and divide by 20, which is the number of dents 
in a score, or beer, and the quotient will be the count, or fine- 
ness of the reed, and if the number of dents in an inch at the 
reed be required, multiply the count of the reed by 20, and 
divide by the given number of inches the reed is set on, and the 
quotient will be the number of dents in an inch, according to the 
fineness of the reed, and the system of counting. 

The system of ascertaining the count, or fineness of reeds for 
lastings, differs from the others, but will be found by multiplying 
the number of dents in an inch by 30, the product of which will 
be the count, or fineness of the reed, and if the number of dents 
in an inch be required, divide the count, or fineness of the reed 
by 30, and the quotient will be the number of dents in an inch, 
according to the fineness of the reed. 

EXAMPLES. 

The count, or fineness of the plain back reed containing 19 
dents in an inch is required: — 

19, dents in an inch. 
54, number of inches the reed is 
set on. 



76 
95 



Score, or beer, 2.0 dents,)102.6 



51.3, or 51 scores, or beers, and 6 
dents set on 54 inches at the reed, or nearly 51J count, or fine- 
ness of the reed. 

What number of dents will there be in an inch of a 51.3 plain 
back reed ? 

51.3, count of reed. 

20 dents, 1 score, or beer. 



No. of inches reed set on, 54)1026.0(19, number of dents in an 

54 inch at the reed. 

486 

486 



WORSTED REEDS. 



WORSTED REED TABLE. 



a 

i-5 

B B 


Scores, or 
beers on 
54 inches. 


Scores, or | 
beers on 
72 inches. 1 


Scores, or 
beers on 
36 inches. 


B ro 
O a> 

% o 

a B 


B • 

— « JS 

03 V 

a .a 

0? — i 

Q 


Scores, or 
beers on 
54 inches. 


Scores, or 
beers on 
72 inches. 


Scores, or 
beers on 
36 inches. 


a of 
o <u 


43. 


116.1 


154.8 


77.4 


1290 


60.5 


163.35 


217.8 


108.9 


1815 


43.5 


117.45 


156.6 


78.3 


1305 


61. 


164.7 


219.6 


109.8 


1830 


44. 


118.8 


158.4 


79.2 


1320 


61.5 


166.05 


221.4 


110.7 


1845 


44.5 


120.15 


160.2 


80.1 


1335 


62. 


167.4 


223.2 


111.6 


1860 


45. 


121.5 


162. 


81. 


1350 


62.5 


168.75 


225. 


112.5 


1875 


45.5 


122.85 


163.8 


81.9 


1365 


63. 


170.1 


226.8 


113.4 


1890 


46. 


124.2 


165.6 


82.8 


1380 


63.5 


171.45 


228.6 


114.3 


1905 


46.5 


125.55 


167.4 


83.7 


1395 


64. 


172.8 


230.4 


115.2 


1920 


47. 


126.9 


169.2 


84.6 


1410 


64.5 


174.15 


232.2 


116.1 


1935 


47.5 


128.25 


171. 


85.5 


1425 


65. 


175.5 


234. 


117. 


1950 


48. 


129.6 


172.8 


86.4 


1440 65.5 


176.85 


235.8 


117.9 


1965 


48.5 


130.95 


174.6 


87.3 


1455 66. 


178.2 


237.6 


118.8 


1980 


49. 


132.3 


176.4 


88.2 


1470 66.5 


179.55 


239.4 


119.7 


1995 

2010 
2025 


49.5 


133.65 


178.2 


89.1 


1485 67. 


180.9 


241.2 


120.6 


50. 


135. 


180. 


90. 


1500 67.5 


182.25 


243. 


121.5 


50.5 


136.35 


181.8 


90.9 


1515 68. 


183.6 


244.8 


122.4 


2040 


51. 


137.7 


183.6 


91.8 


1530 68.5 


184.95 


246.6 


123.3 


2055 


51.5 


139.05 


185.4 


92.7 


1545 J 69. 


186.3 


248.4 


124.2 


2070 


52. 


140.4 


187.2 


93.6 


1560 


69.5 


187.65 


250.2 


125.1 


2085 


52.5 


141.75 


189. 


94.5 


1575 


70. 


189. 


252. 


126. 


2100 


53. 


143.1 


190.8 


95.4 


1590 


70.5 


190.35 


253.8 


126.9 


2115 


53.5 


144.45 


192.6 


96.3 


1605 


71. 


191.7 


255.6 


127.8 


2130 


54. 


145.8 


194.4 


97.2 


1620 


71.5 


193.05 


257.4 


128.7 


2145 


54.5 


147.15 


196.2 


98.1 


1635 72. 


194.4 


259.2 


129.6 


2160 


55. 


148.5 


198. 


99. 


1650172.5 


195.75 


261. 


130.5 


2175 


55.5 


149.85 


199.8 


99.9 


1665173. 


197.1 


262.8 


131.4 


2190 


56. 


151.2 


201.6 


100.8 


1680 73.5 


198.45 


264.6 


132.3 


2205 


56.5 


152.55 


203.4 


101.7 


1695 74. 


199.8 


266.4 


133.2 


2220 


57. 


153.9 


205.2 


102.6 


1710 74.5 


201.15 


268.2 


134.1 


2235 


57.5 


155.25 


207. 


103.5 


1725 75. 


202.5 


270. 


135. 


2250 


58. 


156.6 


208.8 


104.4 


1740 75.5 


203.85 


271.8 


135.9 


2265 


58.5 


157.95 


210.6 


105.3 


1755 76. 


205.2 


273.6 


136.8 


2280 


59. 


159.3 


212.4 


106.2 


1770 


76.5 


206.55 


275.4 


137.7 


2295 


59.5 


160.65 


214.2 


107.1 


1785 


77. 


207.9 


277.2 


138.6 


2310 


160. 


162. 216. 


108. 


1800 


77.5 


209.25 


279. 


139.5 


2325 



384 WORSTED REEDS. 

The count, or fineness of a wildbore reed containing 19 dents 
in an inch, is required : — 

19 dents in an inch. 

72, number of inches the reed is set on. 



38 
133 



Score, or beer, 2.0 dnts.)136.8 



68.4 count, or fineness of the reed, i. e., 

68 scores, or beers, and 8 dents, or 

1368 dents set on 72 inches at the reed. 

What number of dents will there be in an inch of 68.4 wild- 
bore reed ? 

68.4, count of reed. 

20 dents, 1 score, or beer. 



No. of inches reed set on, 72)1368.0(19, number of dents in an 

72 inch at the reed. 



648 
618 



The count, or fineness of a reed, is required from the follow- 
ing particulars : — 

Number of inches the reed is set on, 36. 
Number of dents in an inch, 19. 
Number of dents in a score, or beer, 20. 

19 dents in an inch. 

36, number of inches the reed is set on. 



114 

57 



Score, or beer, 2.0 dnts.)68.4 



34.2, count, or fineness of the reed, i. e., 
34 scores, or beers, and 4 dents, set on 36 inches at the reed. 

If 34 scores, or beers, and 4 dents be set on 36 inches at the 
reed, how many dents will there be in an inch ? 



WORSTED REEDS. 385 

Beers. Dents. 
34 . . 4 
20, number of dents in a beer. 



No. of inches reed set on, 36)684(19, number of dents in an inch 

36 at the reed, 



324 
324 



The count, or fineness of lasting reed containing 19 dents in 
an inch, is required : — 

19 dents in an inch. 
30, number of inches the reed is set on. 



570, or nearly 5f count, or fineness of the reed. 

If a lasting reed contains 570 dents, iiow many dents will 
there be in an inch ? 

No. of inches reed set on, 3.0)57.0 dents. 



19, number of dents in an inch at 

the reed. 

How many dents will there be in an inch of a 50 plain back 
reed? 

50, count of reed. 
20 dents, 1 score, or beer. 



No. of inches reed set on, 54)1000(18.518, or rather more than 

54 18} dents in an inch at the 

reed. 

460 
432 

280 
270 

100 
54 

460 
432 

28 



386 MISCELLANEOUS QUESTIONS. 

JV. B. — Warps are warped quite independent of the set for which 
they may be used. The common way of warping is by portits, 
portives, porters, or beers, tvhichever they may be called. 
Some warp by 48 ends, and lasting warps are generally 
zvarped by 48. Of course it does not matter in what numbers 
they are warped, if the ivarp only contains the number of ends 
required, according to the width and fineness of the reed. 



MISCELLANEOUS QUESTIONS. 

The revolutions a minute of a shaft are required from the fol- 
lowing particulars :-— 

Double strokes of steam engine, 19J per minute. 

Wheel on crank, or fly-shaft, 64 teeth, working into a wheel 49 
teeth on the first line of shafts. 

Wheel 63 teeth on the first line of shafts, works into a wheel 36 
teeth on foot of an upright shaft. Then, wheel 70 teeth on 
the top of the upright shaft, works into a wheel 39 teeth on 
lying shaft ; the speed of which is required. 

Driving-wheels, &c. 

19.5 double strokes, engine makes a minute. 
64 teeth, wheel on fly, or crank shaft. 



780 
1170 



1248.0 

63 teeth, wheel on first lying shaft. 



3744 
7488 



78624 

70 teeth, wheel on top'of upright shaft. 



5503680 dividend. 



MISCELLANEOUS QUESTIONS. 387 

Driven-wheels. 

49 teeth, wheel on first lying shaft. 

36 teeth, wheel on foot of upright shaft. 



294 
147 



1764 

39 teeth, wheel on lying shaft, the speed 
of which is required. 



15876 
5292 



68796 divisor. 

68796)5503680(80 revolutions per minute, speed 
550368 of shaft required. 





Suppose a shaft be making 80 revolutions a minute, with the 
following driving and driven-wheels on the intermediate shafts ; 
what number of double strokes per minute should the engine 
make ? 

Driving-wheels, &c. 

80, revolutions of given shaft per minute. 
39 teeth, wheel on do. 



720 
240 








3120 

36 teeth, wheel 


on 


foot of upright shaft, 


18720 
9360 


on 


the first lying 




112320 

49 teeth, wheel 


shaft. 


1010880 
449280 




5503680 dividend. 





.388 MISCELLANEOUS QUESTIONS. 

Drivenw-heels. 

70 teeth, wheel on top of upright shaft. 
63 teeth, wheel on first lying shaft. 

210 
420 



4410 

64 teeth, wheel on crank, or fly shaft, 



17640 
26460 



282240 divisor. 

282240)5503680(19.5, double strokes of steam- 
282240 engine a minute. 

2681280 
2540160 



1411200 
1411200 



If a drum 42J inches diameter, drives the beaters of a blow- 
ing-machine 1344 revolutions per minute, what must the diameter 
of a drum be, for the beaters to make 1560 revolutions ; and if 
the present drum is to be lagged, what thickness must the lags be ? 

Revols. Inches. Revols. 
If 1344 .• 42.25.-. -1560 
1560 



253500 
21125 
4225 



1344)65910.00(49.04 inches, diameter of drum required. 

5376 
— 5400 

12150 5376 

12096 

. 24 



MISCELLANEOUS QUESTIONS. 389 

49.04 inches, diameter of drum required. 
42.25 inches, diameter of given drum. 



2)6.79 inches, difference of diameters of drums. 

3.395, or nearly 3.4 inches, thickness of lags 

required. 

If a drum 42 J inches diameter drives the beater of a blowing- 
machine 1344 revolutions per minute; what number of revolutions 
will the beater make if driven from a drum 49^ inches diameter? 

Inches. Revols. Inches. 

If 42J or 42.25 .• 1344 .-.- 49.04, or 49 2 V 
49.04 



5376 

120960 
5376 

42.25)65909.76(1560, revolutions of beater a 
4225 minute, nearly. 

23659 
21125 



25347 
25350— nearly. 

If a pulley 13 inches diameter drives the main cylinder of a 
carding-engine, at the rate of 126 revolutions a minute ; what 
diameter must the pulley be, to reduce the speed of the cylinder 
to 112 revolutions? 

126, revolutions given. 
13 inches, diameter of given pulley. 

378 
126 

1638 



390 MISCELLANEOUS QUESTIONS. 

Revolutions req'd, 112)1638(14.625, or 14| inches, diameter of 
112 pulley required. 



518 

448 



700 

672 

280 
224 



560 
560 



How many grains will 30 yards of 3 J hank roving weigh ? 

Hank roving, 3.25)250.00(76.92 grains, or 3 dwts., 5 grains, 
2275 nearly. 



2250 
1950 



3000 

2925 

750 
650 

100 

If 30 yards, or J of a lea weigh 76.92 grains, what hank 
roving will it be ? 

30 yards of roving weigh 76.92)250.00(3.25, or 3J hank roving 

23076 



19240 

15384 

38560 
38460 



100 



MISCELLANEOUS QUESTIONS. 391 

The weight of 1 pair of sets of cops is required from the 
following particulars : — 

Number of spindles in pair of wheels, 1016. 
Length of stretch put up (breakage allowed), 61 J inches. 
Number of stretches, 900. 
Number of yarn 36's. 
1016 x 900 x 61.5 = 56235600.0 dividend. 
840 x 36 x 36 =1088640, divisor. 

56235600 divided by 1088640=51 lbs., 10 J- oz., weight of 

pair of sets. 

How many hanks, leas, and yards, will there be in a pair of 
sets of cops, of which the following are the particulars ? 

Number of spindles in wheels, 808. 

Number of stretches on set, 450. 

Net length of stretch put up, 57J inches. 

808, number of spindles in wheels. 
450, stretches on set. 



40400 
3232 



363600 

57.5, or 57 J inches, lengfh of 
stretch put up. 



1818000 
2545200 

1818000 



r 6)20907000.0 number of inches on pair of 

1 yard, 36 inches, < sets. 

( 6)3484500 

1 lea is 12.0 yards,)58075.0 yards. 

1 hank is 7 leas,)4839 leas, and 70 yards. 



691 hanks, 2 leas, and 70 yards, 
length on pair of sets. 



392 MISCELLANEOUS QUESTIONS. 

If there be 691 hanks, 2 leas, and 70 yards on 1 pair of sets 
of number 36's pincop weft; what weight will they be? 

1 lea is 12.0 yards,)70.0 yards. 



1 hank is 7 leas,)2.5833 leas. 



691.36904 hanks, divided by 36=19 lbs., 
3J oz., weight of 691 hanks, 2 leas, and 70 yards of 36's weft. 

If 20 ounces of cotton were fed on 30 inches of feed-cloth at 
lap-machine, and to pass through all the operations of working 
without loss; what numbers of yarn would it produce, allowing 
the following draughts and doublings? 

437.5 grains, 1 oz. 

20 ounces, weight of cotton fed on 

feed-cloth. 

Draught at lap-machine, 2)8750.0 grains, do. 

Dght. at card, engine, 12.0)437.5 grains, weight of 30 inches of 

lap. 

36.458333 grains, weight of 30 in. 

No. of ends put up at 1st drawing, 6 of carding. 

Dght. 1st hd. of drag., 6.22)218.750000(35 grains weight of 30 

1875 inches, at the 1st head 
of drawings. 

3125 

3125 

35 grs., wgt. of 30 in. of drag. 1st head. 
6, No. of ends put up at 2d hd. of drags. 

Draught at the 2d U 3)2 10(33.33 grains, weight of 30 inches of 
head of drawings, / ^ * ^.^ ^ ^ ^^ 

210 

189 

21 



MISCELLANEOUS QUESTIONS. 393 

33.33 grs. wgt. of 30 in. drug. 2d hd. 
8, number of ends put up at 3d 
head of drawings. 



Dght. at 3d hd. drags., 6.4)266.66(41.666 grs., weight of 30 inches 

256 of drawing at 3d head. 



106 
64 



426 

384 

426 

384 

426 

384 

42 

Dght. at slabbing frame, 5)41.66 grains, weight of 30 inches of 

drawing, 3d head. 

8.33 grs., wgt. of 30 in. of slabbing. 
2, no. of ends put up at rov. frame. 



Draught at roving frame, 7)16.66 



2.38095 grains, weight of 30 inches 

of roving. 

Grains. 
Draught at spinning, 11.5)2.38095(.20704, decimal of a grain 

230 weight, of 30 inches 
of yarns. 

809 
805 



450 

460 — nearly. 
26 



394 MISCELLANEOUS QUESTIONS. 



.20704 grain, weight of 30 inches of yarn. 
36, a multiplier for 30 yards. 

124224 
62112 



7.45344 grains, weight of 30 yards of yarn. 
4 — 4 times 30 yards = 1 lea. 



29.81376 grains, weight of 1 lea of yarn. 

The weight of cotton, according to the foregoing draughts and 
doublings, required to produce 1 lea of yarn is 29.81376 grains, 
or 1 dwt., 5.81376 grains. 

Weight of 1 lea, 29.81376 grns.)1000.00000(33.54 hanks in 1 lb. 

8944128 



10558720 

8944128 


12390400 
11925504 


16145920 

14906880 


464896 


33.54 hanks = lib. 
8.385 hanks = 4 ounces. 




41.925 hanks = 20 ounces. 
7 leas = l hank. 




293.475 

29.8137 grains =1 lea. 




2054325 
880425 
293475 
2347800 
2641275 
586950 





8749.5756075 grains weight, or 20 ounces 
fed on 30 inches of feed cloth at lap machine. 



MISCELLANEOUS QUESTIONS. 395 

If 20 ounces of cotton fed on 30 inches of feed cloth at lap 
machine produces number 36's twist, or weft, according to the 
following draughts and doublings ; what will the loss sustained 
in working be ? 

Draught at the lap machine, 2. 
Draught at the carding engine, 120. 
Draught at the 1st head of drawings, 6.25. 
Draught at the 2d head of drawings, 6.3. 
Draught at the 3d head of drawings, 6.4. 
Draught at the slabbing frame, 5. 
Draught at the roving frame, 7. 
Draught at the spinning, 11.5, 
Multiplier for 30 inches, 6.944. 

Doublings at the 1st head of drawings, 6. 
Doublings at the 2d head of drawings, 6. 
Doublings at the 3d head of drawings, 8. 
Doublings at the roving frame, 2. 
Numbers of yarn produced, 36's. 

Draughts. 

2, lap machine. 
120, carding engine. 



240 
6.25, first head of drawings. 

1200 

480 
1440 

1500.00 
6.3, second head of drawings. 

4500 
9000 



9450.0 

6.4, third head of drawings. 



37800 
56700 



396 MISCELLANEOUS QUESTIONS. 

60480.0 

5, slabbing frame. 



302400 

7, roving frame. 



2116800 

11.5 mules. 



10584000 

23284800 



24343200.0 
Mult, for 30 in., as per table,6.944 

97372800 
97372800 
219088800 
146059200 



169039180.800 dividend. 

Doublings. 
6x6x8x2x36= 20736 divisor. 

169039180.8 divided by 20736 =8152 grains, or 18 oz., 11 dwt., 
18 grains, weight of yarn produced from 20 oz. of cotton. 

oz. dwts. grs. 
Weight of cotton fed on feed cloth at lap machine, 20 . . . . 
Weight of yarn produced, . . . . 18 . . 11 . . 13 

Loss sustained in working, . . . . 1 . . 6 . . 16.5 

Suppose there be a 48 teeth wheel working into a 36 teeth 
wheel, and finding them of a finer pitch than they should be ; 
what wheels will work in the same place to produce the same 
speed with the same diameters of wheels ? 

RULE. — Reduce the wheels to their lowest terms, by dividing 
them by any number that will divide the number of teeth in 
the wheels without a remainder ; then multiply the lowest terms 
of the wheels by any one number that will produce the number 
of teeth required. 



MISCELLANEOUS QUESTIONS. 




Thus, 




12)48 




12)36 


jowest term, 4 




3 lowest term. 


Lowest term, 4 

2 




3 lowest number. 

2 


Wheel, 8 teeth, 


and wheel 6 teeth. 


Lowest term, 4 
3 




3 lowest term. 
3 


Wheel, 12 teeth 


, and wheel 9 teeth. 


Lowest term, 4 

4 




3 lowest term. 
4 



397 



Wheel, 16 teeth, and wheel, 12 teeth. 

Lowest term, 4 3 lowest term. 

5 5 

Wheel, 20 teeth, and wheel, 15 teeth. 

Lowest term, 4 3 lowest term. 

6 6 

Wheel, 24 teeth, and wheel, 18 teeth. 

Lowest term, 4 3 lowest term. 

9 9 

Wheel, 36 teeth, and wheel, 27 teeth. 

1W.B. — The same system will answer, either for increasing or 
decreasing the number of teeth in wheels. 

Any of the above wheels working together will produce the 
same speed. 



398 JUDKINS' AMERICAN HEALDS. 



JUDKINS' AMERICAN HEALDS, OR PATENT 
HEDDLES. 

PLATE I. 

The machine shown in the drawing is so constructed as to 
double and twist the yarn from single of itself, and at the same 
time, at certain points, is converted into a braiding or platting 
machine, by which the eye or loop of the heddle is formed, with- 
out knots of any description. 

The advantages of this machine are many. A set of healds is 
produced by it at a much less cost than by any other method, and 
without a single knot at any point, the whole being one continu- 
ous twine or cord. 

By the drawing is also shown a set of healds made by this 
machine, with the eye or loop as described, which is coated, lined, 
or covered with a metallic substance, suitable for the purpose. 

One set of patent healds will last fifteen of any other kind, 
and a greater number of yards of cloth, heavier and more perfect, 
can be produced through it, in a given time, in consequence of 
less friction upon the warp. 



mason's self-acting mule. 399 



MASON'S SELF-ACTING MULE. 

PLATES II. III. IV. V. 

Of this machine we give the inventor's specification complete : 

The schedule referred to in the letters patent and making part 
of the same. 

To all to whom these presents shall come — Be it known, that 
I, William Mason, of Taunton, in the County of Bristol and 
State of Massachusetts, have invented a new and useful self-acting 
mule for spinning cotton and other fibrous substances, and that 
the following is a full, clear and exact description of the principle 
or character which distinguishes it from all other things before 
known, and of the manner of making, constructing and using the 
same, reference being had to the accompanying drawings, making 
part of this specification, in which Fig. 1 is an elevation of the 
head of the mule next the carriage — Fig. 2 an elevation of the 
opposite side — Fig. 3 a plan — Fig. 4 a back elevation — Fig. 
5 a longitudinal vertical section taken at the line (XX) of Fig. 
3, looking in the direction of the arrow — Fig. 6 a front eleva- 
tion — Fig. 7 a section of, and through the friction clutch — Fig. 
8 separate view of the scroll or volute cam — -and Fig. 9 a ver- 
tical cross section of the head taken just in front of the shipper 
lever. The same letters indicate like parts in all the figures. 

The motions of the mule may be divided into three series, which 
are subdivided in the action of the apparatus. The first series 
consists of the drawing out of the carriage, the revolving of the 
draw-rollers and the whirling of the spindles, by means of which 
series of motions the rovings are drawn out and the threads spun 
and twirled. The second series consists of backing off, as it is 
termed, that is, turning the spindles the reverse direction, to un- 
coil the threads from the points of the spindles to the cops and 
turning down or depressing the front faller, at the same time to 
place all the parts in a proper condition for the third series of 
motions, which consists of putting or running in the carriage, 
winding on the yarn or threads by giving a varying motion to the 
spindles corresponding to the form and size of the cops, and ope- 
rating the faller to give the proper shape to the cops. 



400 mason's self-acting mule. 

The first series of motions is regular. The carriage is drawn 
out by a regular motion, effected by a train of wheels from the 
driving pulley to a line shaft, which carries endless chains con- 
nected with the carriage at different parts of its length to insure 
steadiness of motion. During this the draw-rollers are rotated, 
to give out the staple as it is spun by another train of wheels 
deriving motion from the same source as the preceding, and in a 
manner substantially similar to other mules. And at the same 
time the spindles are whirled or rotated by a band receiving mo- 
tion from a pulley on the shaft of the driving pulley as in other 
mules. This completes the first series of motions, in which I 
claim nothing new. 

At the end of the first series of motions, the threads that have 
been spun are coiled on the spindles from the cops to their points 
— it is therefore necessary to uncoil them (called "backing off") 
preparatory to winding on, and at the same time to depress the 
front faller to place it in a proper position for winding on. The 
second series of motions effects these purposes, and the various 
parts of the mechanism are put in a proper condition to effect 
this by the momentum of the moving parts at the end of the first 
series of motions. This constitutes the first part of my invention. 
As the carriage approaches the end of the out motion, the driving 
belt is shifted from the first driving pulley to a loose pulley by 
the side of it, to permit the momentum of the moving parts to 
complete the movements, and so soon as these are accomplished 
a balance weight is carried beyond the vertical line and falls over, 
which shifts the belt from the loose pulley to a second fast pulley 
on the same shaft with the others, at the same time the trains of 
wheels that operate the carriage and the draw-rollers are liberated 
by the shifting of a clutch, and at the same time a friction clutch 
is brought into action, thereby connecting the band that drives 
the spindles with a sliding rack (called the " top-sliding rack") 
which, in consequence of this connection, is carried by the mo- 
mentum of the spindles sufficiently far in one direction to give 
by its return the required motion to the spindles in the reverse 
direction to uncoil the threads from the upper parts of the 
spindles. Whilst the rack is thus moved, the second fast pulley 
sets in motion, by a train of wheels, a crank pin that works in a 
slot in a connecting rod, and this crank pin when set in motion 
is a little below a line passing through the connecting rod and the 
axis of motion, so that the crank pin moves a short distance before 
it begins to move the connecting rod — this period of time is suffi- 
cient to permit the momentum of the spindles (as above stated) 



mason's self-acting mule. 401 

to draw the sliding rack to the distance required to be in a con- 
dition, by its return movement, to give the "backing-off" motion 
to the spindles. The crank pin then in making a semi-revolution 
carries the connecting rod with it, and this being in connection 
with the lever of a rock shaft, provided with a toothed pulley, 
around which passes a chain attached to the end of the sliding 
rack, draws it (the rack) for a short distance in a reverse direction, 
and thus causes it to give the backing-off motion to the spindles, 
to uncoil the threads, at the same time depressing the front faller 
to bring the threads in a proper position for winding on, this latter 
being effected by having one end of the shaper or coping rail 
jointed to a lever on the rock shaft above-mentioned. The chain 
attached to the rack and which communicates motion to it, is kept 
tight by being passed over a pulley and having a weight suspended 
to it. 

"When the top-sliding rack is carried forward by the momentum 
of the spindles at the end of the first series of motions, it is gra- 
dually arrested, and with it the spindles, by means of a spring 
brake of a peculiar construction, viz. : — On the rock shaft there 
is a bent lever, to one end of which is connected a helical spring 
also attached to an arm jointed to the other end of the bent lever : 
and by the side of and attached to, the toothed wheel, around 
which passes the chain on the end of the sliding rack, and which 
turns freely on the rock shaft, there is a ratchet wheel and by 
the side of it a cam plate provided with a hand or catch, by 
means of which the ratchet and toothed wheels are carried around, 
when the cam plate is carried around by the action of the spring 
brake on the cam form of its periphery. And when this has 
been carried far enough around, the catch is liberated to permit 
the return of the parts by means of an arm or lever jointed to 
one end of the bent lever which is made to lift the catch from 
the teeth of the ratchet wheel. As the cops increase in diame- 
ter, it is evident that the backing-off motion must be diminished, 
and this is effected by making the connecting rod above-mentioned 
in two parts, the first connected by one end (as above stated) with 
the crank pin which actuates it and which works in a slot to give 
motion to the rod in one direction only (the crank being then at 
liberty to turn without imparting any motion longitudinally to the 
rod), the other end being jointed to a curved arm that vibrates 
on a stud pin, and the other part of the connecting rod is jointed 
to the arm of the rock shaft and to a slide that works in a curved 
groove in the vibrating arm, so that as this slide is moved from 
or towards the axis of motion of the arm, the rock shaft will be 



402 MASON'S SELF-ACTING^ MULE. 

vibrated more or less and this slide is moved in or out by being 
in connection with the mechanism that operates the motions of 
the coping rail, and which will therefore be described under the 
third series. At the end of the backing-off motion, the vibrating 
arm of the connecting rod is hooked and held by a catch until 
the carriage is run up, and then liberated to permit the parts to 
resume their appropriate positions preparatory to a repetition of 
the operation. 

At the end of the second series of motions the third series of 
motions commences, and these constitute the second part of my 
invention. The carriage is run in by a crank motion, which has 
the effect to gradually start it from a state of rest, and accele- 
rate its motion to the middle of its course, and then gradually 
diminish its motion until it is brought to a state of rest — thus 
avoiding all tendency to break the threads consequent upon all 
sudden motions. This is effected in the following manner, viz. : 
When the shipping lever is operated at the end of the first series 
of motion, a clutch on a shaft carried by the second fast pulley 
is shifted, and on this clutch has but one tooth, the shaft is there- 
by permitted to make part of a revolution, during which the 
second series of operations takes place before it (the clutch) be- 
gins to act, and then it communicates motion to a large cog- 
wheel provided with a crank pin, that actuates a connecting rod 
jointed to a rack (below the top-sliding rack above described), 
the teeth of which take into the teeth of a pinion on the shaft 
of one of the train of wheels that communicate motion to the 
carriage, thereby imparting the desired movement. The wind- 
ing on of the yarn during the running in of the carriage is ef- 
fected by the top sliding rack, which for the purpose is carried 
by the rack just described, by means of such connections as ad- 
mit of modifying the motions of the top-sliding rack which drives 
the spindles in winding on. Motion is communicated from the 
bottom to the top rack in the following manner : — On the end 
of the lower rack and by the side of it, there is a stud pin 
on which turns a scroll cam, and to that part of its periphery 
which is nearest the axis is attached one end of a chain, which 
passes from thence around a roller that turns on a stud pin at 
the side of the lower rack, and is then carried back and attached 
by a short arm to the top-sliding rack, so that when the lower 
rack slides the top rack will move with it, provided the scroll 
can remain immovable on its axis, but as the motion of the top 
rack during each operation must have a motion accelerated rela- 
tively to that of the lower rack, to increase the rotation of the 



mason's self-acting mule. 403 

spindles, as the threads are ■wound on a gradually diminishing 
diameter of the conical form of the cops — this is effected by 
causing the scroll cam to turn on its axis during the motion of 
the rack, by having a wheel attached to and turning with it, to 
the periphery of which is attached one end of a chain, that 
passes around it, and is attached by the other end to another 
part of the machine, so that if this part of the attachment re- 
mains fixed, a regular accelerated motion will be given to the 
top rack, relatively to the motion of the lower rack, and neces- 
sarily the spindles will have their rotation accelerated relatively 
to the motion of the carriage. These relative motions of the 
two racks, as described, are such as are required after the base 
of the cops has been formed, for then the threads are wound 
regularly on a cone : but in forming the base of the cops the 
first winding is on the naked spindles, at which time the motion 
of the spindles should correspond with that of the carriage, and 
from the commencement until the base is formed, the accelerated 
motion should be gradually brought into play, to give the conical 
form to the cops. This is effected by having the chain that 
winds on the wheel that turns with the scroll cam, attached to a 
slide that works on a screw in a vibrating arm, the outer end of 
which is jointed to another arm of equal length, that turns on 
the end of the stud, on which the scroll cam and wheel turn, so 
that when the slide is at the lower end of the arm, the two arms 
being of equal length, the motion of the wheel with the rack will 
not cause it to wind up the chain, but, as the slide is drawn up 
towards the axis of vibration of the arm, one end of the chain 
will necessarily move through a less space than the other, and 
thus cause the wheel, with the scroll cam attached thereto, to 
turn on its axis, and thus to vary the motion of the top rack, 
and thereby adapt the motion of the spindles to the varying 
diameter of the base of the cops. The screw in the vibrating 
arm that carries the slide, is in connection by means of appro- 
priate cog-wheels with a horizontal ratchet wheel, which is free to 
move when the arm vibrates in one direction, but held by the 
hand or catch when the arm vibrates in the reverse direction, 
for the purpose of turning the screw to move the slide : and this 
hand or catch is governed by an apparatus called a butterfly, 
which is acted on by an arm from the counter-faller, when the 
tension of the thread is too great, and thus throws the hand into 
the teeth of the wheel, that the vibration of the arm shall ope- 
rate the slide — the hand or catch being disengaged at each run- 
niog out -of the carriage. The last of the third series of mo- 



404 mason's self-acting mule. 

tions is the operation of the coping rail for operating the faller, 
which being essentially similar to others, needs no special notice 
here. 

At the end of the running in motion of the carriage, a pin on 
an arm projecting from the shaft of the crank that operates, the 
under rack liberates the catch that holds the connecting-rod, by 
which the backing- off motion is effected, and so soon as it is 
liberated, the weight of the machinery attached draws it back 
— and to prevent any sudden jar by this operation, the crank 
pin which operates the connecting rod in one direction, is so 
governed in its revolutions as to be nearly a semi-revolution from 
its point of departure, at the commencement of the backing-off 
operation, so that the force required for carrying it back to this 
position is sufficient to ease off the motion of the returning parts. 
This crank pin is held in the position just indicated by a brake 
within the second fast pulley, and this brake is connected by a 
joint link and lever with the arm of the connecting-rod of the 
backing off apparatus, which, when drawn back, forces the brake 
in contact with the pulley, and arrests the train of wheels and 
this crank pin in their appropriate place. 

When finishing the caps it is important to wind the threads on 
tight at the point, particularly as the upper ends of the spindles 
are tapering. This is effected by forming the connection between 
the chain and the end of the top sliding rack by means of a vibrat- 
ing frame, from which projects another arm that has a chain 
jointed to it, extending to and winding on an arbor, which arbor 
has a ratchet-wheel on it, which is carried a part of a revolution 
at each operation of the mule by a hand on the arm of the con- 
necting rod of the backing-off motion ; and this auxiliary chain is 
of such length that it continues to be wound upon the arbor with- 
out affecting the operations of any part of the machinery until 
the caps are nearly completed, and then it becomes so short as to 
be brought in contact with a permanent arm towards the end of 
the winding-on operation, and when thus brought in contact with 
this arm it suddenly shortens the chain that forms the connection 
between the two racks, and necessarily increases the rotation of 
the spindles, which, as a necessary consequence, draws the threads 
tighter on the spindles. 

In the accompanying drawings (A 3 ) represents a frame pro- 
perly adapted to the operative parts of what constitutes the head 
of the mule, the carriage not being represented, as it is in every 
particular similar to other mules. (A A 1 A 11 ) are three pulleys 
of equal diameter and placed side bj side on the main shaft (B), 



mason's self-acting mule. 405 

The one (A) is the first fast pulley attached to, and turning with 
the shaft (B). (A 1 ) is the second fast pulley, carrying a pinion 
(D), and turning freely on the shaft (B), and (A 11 ) is a loose pulley 
placed between the other two and turning freely on the shaft. 
A driving belt from some first mover passes over these pulleys and 
is guided to either of them by a shipper lever (C) that vibrates on 
a steel pin (W), and connected with a weighted balance lever (C 3 ), 
by which it is operated when the belt is to be shipped from one 
to another of these pulleys. [At the commencement of the first 
series of operations, the belt runs on the first fast pulley (A 1 ), to 
give the first series of motions. The pinion (J) on the shaft (B) 
communicates a positive and regular motion to the shaft (G), 
(which is in connection with the draw rollers in the usual manner), 
by means of the first train of wheels (K, L, J), and from the 
shaft (G) by the second train of wheels (N, 0, P, R, S, X), to 
the line shaft (Y) that drives the carriage by means of endless 
chains (Z) connected with the carriage by one of the links (Z 3 ). 

There is but one of these chains represented in the drawings, 
and the shaft is shown as broken off, as the connections with the 
carriage present nothing new, and therefore need not be repre- 
sented. And at the same time the spindles are rotated or whirled 
by the usual band (T 1 ), driven by the pulley (O 1 ), on the same 
pulley shaft (B). This completes the first series of motions, 
viz : drawing out the carriage, rotating the draw rollers, and 
whirling the spindles, to draw out, spin and twist the threads. 

Towards the end of the running out motion of the carriage, 
the belt is shipped from the first fast pulley (A) to the loose pulley 
(A 11 ) which removes the driving power from these motions. This 
shifting of the belt is effected in the following manner, viz : the 
weighted balance lever (C 3 ) is jointed to the shipper lever at 
(2), and above the stud pin (3), on which it vibrates, its upper 
end being weighted to enable it to fall over by gravity, after the 
weight has been carried a little beyond the vertical line. The 
lower end of this balance lever is T formed, and one of its short 
arms is jointed by a link (4), with a short lever (5) that turns on 
a stud pin (6), and this lever is also connected by a link (d) with 
another lever (A) that turns on a stud pin (c), and this last lever 
is depressed when the belt is to be slipped by means of a pin (a) 
in a vibrating arm (L 1 ) on the shaft (K 1 ) of the wheel that carries 
the connecting rod by which the carriage is run in. The balance 
lever is by this means carried a little beyond the vertical line, 
and then carried entirely over by the weight of the lever (C 3 ). 
On this same shaft (K 1 ), and on the opposite side of the frame 



406 mason's self-acting mule. 

there is another arm (M 1 ) provided with a pin (g), which at the 
same time depresses another lever (N 1 ), converted by means of a 
jointed rod (h) with an elbow lever (7) that operates a clutch (M) 
on the shaft (G) by means of which the cog-wheel (I) is clutched 
to its shaft, or unclutched, so that when the driving belt is re- 
moved from the fast pulley (A) to disconnect the parts that give 
the first series of motions to the wheel (I) is unclutched, which libe- 
rates the draw rollers, and the second train of wheels that com- 
municate motion to the carriage from the parts that drive the 
spindles, so that they (the spindles) are free to continue to move 
by their momentum independents the draw rollers and carriage. 
The clutch (M) is held open until the belt is again carried to the 
first fast pulley at the end of the third series of motions by a 
pin (j 1 ) in one arm of the balance lever (C 3 ) which bears against 
one side of the arm of the clutch lever (7), for the lever (N 1 ) that 
operates the clutch lever is provided with a helical spring (i) 
attached to it and the frame, for the purpose of forcing the clutch 
in the moment that the pin (/) of the balance lever (C 3 ) liberates 
the clutch lever (7). The parts being thus situated, and the 
driving belt in the loose pulley, the momentum of the spindles 
will cause them to continue to turn for some time, and thus com- 
mences the second series of motions. 

The band (T 1 ) that carries the spindles, and which, as stated 
above, passes around and is carried by the pulley (O 1 ) on the main 
shaft (B), passes around a guide pulley (R 1 ) at one end of the 
frame, and another (S 1 ) at the other end, and also around another 
pulley (P 1 ) that runs freely on a shaft (Q 1 ), except when clutched 
to it, which is done at the time the driving belt is slipped from 
the first fast pulley (A). This pulley (P 1 ), called the "friction 
clutch pulley," is a hollow cone lined with leather, into which is 
received a conical friction clutch (P 11 ) attached to the end of the 
shaft (Q 1 ), which slides endwise in its bearings, and in the friction 
pulley, which is prevented from sliding endwise with the shaft by 
a collar (8); so that, when this shaft (Q 1 ) is moved in one direc- 
tion, the pulley (P 1 ) is clutched to it by the friction of the conical 
surfaces, and when moved in the reverse direction, it is unclutched, 
and turns freely on the shaft. This clutching and unclutching 
is effected by an arm (Z 2 Fig. 5), on the spindle (U 1 ) of the shipper 
lever (C), which embraces a collar on the shaft (Q 1 ), so that when 
the shipper (C) shifts the belt from the first fast pulley (A), it at 
the same time gives the requisite movement to clutch the friction 
clutch that connects the spindles with the shaft (Q 1 ), which will 
be carried by their momentum, and as this shaft is connected by 



mason's self-acting mule. 407 

the train of wheels (X 1 , Y 1 , Z 1 and C 11 ), with a horizontally sliding 
rack (W 1 ), it (the rack) will be carried for a short distance in the 
direction of the arrow thereon. See Fig. 5. When the shipper 
transfers the belt from the first fast to the loose pulley, a clutch 
(D 2 ) Fig. 9, on the shaft (D 1 ) is shifted by the forked lever (/), 
which turns on the stud pin (10), and is operated by a spur (11) 
on the balance lever (C 3 ), which bears on the end of a volute 
spring (12) attached to the lever (/), the tension of which forces 
the sliding part of the clutch against the permanent part, which, 
having but one cog, causes it to clutch, when by the rotation of 
the shaft the parts coincide. The sliding part of the clutch is 
feathered to the shaft (D 1 ), which is carried by a train of wheels 
(C 1 B 1 ), and pinion (D), on the second fast pulley (A 1 ), driven by 
the driving belt, when it is shifted by the shipper, which carries 
it from the first fast pulley (A) to the loose pulley (A 11 ), and then 
to this, the time required for this transfer of the belt by the mo- 
tion of the shipper being sufficient for the preparatory movements. 

So far, it has been shown, that the second fast pulley carries 
the shaft (D 1 ) of the clutch (D 2 ) a part of a revolution, before 
clutching the pinion (E 1 ) which gears into the wheel (F 1 ) that 
runs the carriage in (as will be hereinafter described), this period 
of time being required to enable the momentum of the spindles 
to run back the rack (W 1 ) preparatory to the backing-off motion. 

As the rack (W 1 ) is carried by the momentum of the spindles 
in the direction of the arrow, preparatory to the backing-off mo- 
tion, it is necessary gradually to arrest this motion, which is 
effected by a friction-spring brake, constructed and connected 
with the rack in the following manner. To the end of the rack 
is attached a chain (m), which passes over a pulley (o), and then 
around a spur-wheel (p), attached to a ratchet-wheel (H 2 ), and 
with it turning freely on a rock-shaft (n), and then it passes over 
another loose pulley (D 3 ), and to the end of it is suspended a ten- 
sion weight (E 2 ), which takes up the slack of the chain. On the 
said rock-shaft (n), and by the side of the ratchet-wheel, there is 
a cam plate (£), that also turns freely on the shaft, and which is 
carried in one direction by the ratchet-wheel, when the catch or 
hand (t>), which is jointed to the cam-plate, takes into the teeth 
of the ratchet, the two turning independently of each other in 
the reverse direction, or in the same direction, when the catch or 
hand is lifted out of the teeth. When the rack is drawn by the 
momentum of the spindles in the direction of the arrow, the 
chain (m) attached thereto turns the spurs and ratchet-wheel in 
the direction of the arrow, and the cam-plate is also turned in 



408 mason's self-acting mule. 

the same direction, by the catch or hand (v); this motion is gra- 
dually arrested by the enlarged or scroll-form of the cam-plate, 
which forces out a friction arm (b 1 ), one end of which is jointed 
at (a 1 ), to one arm of a lever (F 3 ) attached to the rock-shaft (w), 
the other arm of this lever being connected with the friction arm 
(I 1 ) by a helical spring (S), it will therefore be perceived, that as 
the friction-arm is forced out by the cam-plate, the tension of the 
spring increases the friction of the brake on the periphery of the 
cam-plate, which gradually arrests the motion of all the parts in 
connection with the rack (W 1 ), and of necessity the spindles. 
When these parts are arrested, the rock-shaft (n) is turned in the 
opposite direction, and carries with it the cam-plate, ratchet- 
wheel, and spur-wheel by the pressure of the brake, and of ne- 
cessity reverses the motion of the rack and spindles to uncoil 
the threads from the spindles. At the end of this motion, the 
catch (v) of the cam-plate is liberated from the ratchet-wheel 
(H 2 ) by a spur (x) of a lever (y) jointed at (14), to the arm (F 3 ) 
of the rock-shaft {n\ the spur being forced on to the back end 
of the catch by the rotation of the rock-shaft, the lever (y) hav- 
ing a slot in it which turns and slides upon a permanent rod (z). 
This reversed motion of the rock-shaft (n) is effected by a crank 
motion in the following manner, viz. : The pinion (D) on the second 
fast pulley (A 1 ) communicates motion by the train of wheels (B 1 
C 1 and R 2 ) to the wheel (Q 2 ) in the direction of the arrow, and 
this wheel carries a crank pin (A 1 ), that works in a slot (A 2 ) of a 
connecting rod (0 2 ), jointed to a curved arm (K 2 ) that vibrates 
on a fixed stud-pin (15), and this arm has a slot in it which works 
a slide (e 1 ), for the purpose of graduating the backing off motion, 
and to this slide is jointed another connecting rod (J 2 ), the other 
end of which is jointed to the arm (I 2 ) of the rock-shaft (n). At 
the time that the driving belt is shifted to the second fast pulley 
(A 1 ), which takes place while the momentum of the spindles pre- 
pares the parts for the backing-off motion, the crank pin (A 1 ) is 
at (A 3 ), a little above a line passing from the centre of the wheel 
to the junction of the connecting rod (O 2 ) and the arm (K 2 ), so 
that the crank pin on this wheel can move around to the position 
represented in Fig. 2, before it begins to draw the connecting rod, 
to give time for completing the preparation of the parts for back- 
ing off. In rotating from (h l ) to (A 4 ), the crank pin carries the 
connecting rod the required distance to give the required backing- 
off motion to the spindles to uncoil the threads, and at the same 
time depresses the faller to guide the threads to the cops, prepa- 
ratory to winding on by means of the coping rail or former (G 2 ), 



mason's self-acting mule. 409 

one end of which is connected by a slot with a wrist (q) on an 
arm (F 2 ) of the rock-shaft (n), the elevation of which by the back- 
ing-off motion of the rock-shaft (w) depresses the faller. So soon 
as the connecting rod (o 2 ) has been carried to the point (h 4 ) by 
the crank pin, which is the extent of the backing-ofF motion, the 
catch lever (U 2 ) takes hold of the pin (13) on the arm (K 2 ), and 
there holds all the parts of the backing- off operation until re- 
leased towards the end of the running- in motion of the carriage, 
the liberation of the parts being then effected by means of a pin 
(I 1 ) on the arm (L 1 ) on the shaft (K 1 ) of the wheel (F 1 ), which 
runs in the carriage. So long as the backing-off apparatus is 
held by the catch lever (U 2 ), the crank pin (h 1 ) can revolve freely, 
the slot in the connecting rod (O 2 ) admitting of this. When the 
backing-off apparatus is liberated, it falls back to the position 
indicated in the drawings by the weight of the coping rail and 
the other parts attached to the rock-shaft; and to prevent jar, 
this return motion of the parts is eased off by the connecting rod 
(O 2 ), coming against the crank pin (h l ) at the point (A 3 ), the power 
required to turn this train of wheels in the reverse direction being 
sufficient to ease off and gradually arrest the moving parts without 
jar. This return motion of the backing-off apparatus at the same 
time arrests the second fast pulley (A 1 ) and the train of wheels 
in connection with it, by means of a brake (j 1 ) connected by the 
arm (T 2 ), and link (S 2 ) with the arm (K 2 ) of the backing-off ap- 
paratus, and the train of wheels and the connection of the brake 
are so regulated as to stop the crank pin (h 1 ) at the point (h 3 ), 
where it is required to be when the second series of motions is 
commenced. The link (S 2 ), and the connecting rod (J 2 ), are pro- 
vided with adjusting screws for the proper adjustment of all these 
parts. 

As the backing-off motion must be gradually decreased as the 
cop is formed and increased in length, the vibrating motion of 
the rock- shaft is gradually shortened by means of the slide (e 1 ) 
in the arm (K 2 ) to which the connecting rod (J 2 ) is jointed. 

For this purpose, the slide is attached to a chain (d l ), which 
passes over the upper end of the arm, and is gradually wound 
upon the arbor (e u ) of a cog-wheel (L 2 ) that gears into a pinion 
(f 1 ) of a ratchet-wheel (N 2 ), which receives motion from the 
vibration of the arm (K 2 ) of the backing-off apparatus, by a hand 
or catch (M 2 ) jointed thereto at (g l ). It will be evident that, as 
the slide is drawn up by the chain towards the axis of motion of 
the arm (K 2 ), the motion of the connecting-rod (J 2 ) will be di-. 
minished, and with it the motion of the backing-off apparatus. 
27 



410 mason's self-acting mule. 

This completes the second series of motions, and the mule is 
then in a condition to commence the third series. 

When the clutch (D 2 ) at the end of the backing-ofF motion 
clutches the pinion (E 1 ), it begins to turn, which communicates 
motion to the cog-wheel (F 1 ) on the shaft (K 1 ) ; and to the 
periphery of this wheel at (G 1 ), is jointed a connecting-rod (H 1 ), 
the other end of which, at (I 1 ), is jointed to a horizontal sliding- 
rack (Y) that runs on ways (W), that carries, by means of the 
pinion (U), the train of wheels that communicate motion to the 
carriage. The wheel (F 1 ) is carried but part of a revolution 
(nearly one-half) in one direction by its connection with the 
second driving-pulley (A 1 ), when the clutch (D 2 ) is closed, which 
gives, by the crank-motion in consequence of the connection 
above pointed out, the peculiar running-in motion to the carriage, 
as pointed out in the description of the general characteristics of 
this invention; and, as the carriage approaches the end of its 
running-in motion, the pinion (E 1 ) is unclutched by the reversed 
action of the shipper-lever (C 3 ), this reversed motion of the ship- 
per and its appendages being effected by the pin (e) on the arm 
(L 1 ) of the shaft (K 1 ) of the wheel (F 1 ), this pin (e) being on the 
side of the shaft (K 1 ) opposite to the pin (a) which first ships it. 
The unclutching of the pinion (E 1 ) leaves the wheel (F 1 ) free to 
be turned back by the reversed motion of the rack (Y) by the 
train of wheels which run out the carriage in the first series of 
motions. 

As the carriage is run in by the means just described, the 
spindles must be turned to wind up the threads which have been 
spun during the first series of motions, and this is effected by 
means of the top sliding-rack (W 1 ), by which the backing-off 
motion is given, and which is placed on' top of the main rack (V). 
The connection of this rack (W 1 ) with the spindles, by means 
of the friction-clutch, having been described, it is only necessary 
to describe the manner in which the winding-on motion is com- 
municated to it by the main rack (V), and the manner in which 
this motion is varied and regulated to correspond with the vary- 
ing size of the cops as they are formed. To the upper rack (W 1 ), 
and near one end of it, is jointed a lever (m 1 ), to the short arm 
of which is attached a chain (I 1 ), which thence passes around a 
pulley (k 1 ) that turns on a stud-pin projecting from the side of 
the main rack (Y), the other end of the said chain being attached 
to the smallest diameter of a scroll-cam (n l ) connected with the 
end of the main rack (Y). From this arrangement it will be 
obvious that if the cam [n) be prevented from turning on its 



mason's self-acting mule. » 411 

axis, the motion of the main rack (V) will carry the top rack in 
the same direction and with the same varying velocity, which 
would give to the spindle a winding-on motion corresponding 
with the running-in motion of the carriage, such as would be 
required if the cops were to be formed cylindrical and did not 
vary in diameter ; but such is not the case, as clearly pointed 
out in the general description. To give the varying motion 
required and fully pointed out above, the scroll-cam (n 1 ) is 
attached to and turns with a wheel (v) on the stud-pin (I 1 ) on 
the main rack (V), and to this wheel, at (w), is attached a chain 
(x 1 ), which, after passing around a portion of the circumference 
thereof, is attached by a link (y l ) to a slide (z 11 ) that travels on a 
screw (a 11 ) that turns in the arm (V 2 ) of a rack-frame (V 3 ), the 
lower end of the said arm being jointed to another arm of equal 
length (W 2 ) that vibrates on the stud-pin (I 1 ) on which turn the 
wheel (v 1 ) and the cam (w 1 ), so that when the slide (z 11 ) is at the 
lower end of the arm (V 2 ), that end of the chain (x 1 ) which is 
attached to the slide, during the movements of the main rack, 
will not communicate motion to the wheel (v l ) and cam (n 1 ) ; 
hence the motions of the two racks (V) and (W 1 ), will correspond 
and give to the spindles the motion required for winding the 
threads on the naked spindles, and, as the base of the cops is 
increased in diameter, the slede (z 11 ) is drawn up towards the 
axis of motion of the arm (V 2 ) to decrease the motion of that 
end of the chain (x 1 ) attached to it, which will cause the wheel 
and cam to turn on their axis, and thus give out the chain (Z 1 ), 
thereby giving to the top rack (W 1 ), and, consequently, to the 
spindles, a gradually reduced motion relatively to the main rack 
to correspond with the increased diameter of the base of the 
cops. The motion required is given to the slide (z 11 ) by the 
vibrations of the rock-frame (Y 3 ), the screw (a 11 ) that operates 
the slide being connected by a train of cog-wheels (b 11 , e x \ g x \ 
h 11 , i 11 , j n ), with a horizontal ratchet-wheel (I 11 ), which turns 
freely by the rocking motion of the frame (V 3 ) in one direction, 
and which, therefore, does not turn the screw but which is pre- 
vented from turning in the opposite direction (during the running- 
in motion of the carriage) by a catch or pawl (r 11 ) to turn the 
said screw. 

Whenever the tension of the threads in winding on is too 
great, it bears down the counter-faller (not represented in the 
drawings), the arm of which in the running-in motion of the 
carriage strikes an arm (S 11 ) of what is termed a butterfly, 
that turns on a stud pin (q ir ), on which the catch or hand (r 11 ) 



412 mason's self-acting mule. 

of the ratchet (I 2 ) also turns, and with which it is connected by 
a spring (w 2 ), (see Fig. 1), and throws it into the teeth of the 
ratchet-wheel — the wheel being thus held, the farther vibration 
of the rock-frame turns the screw, and carries up the slide to re- 
duce the motion of the spindle, and on the return motion of the 
carriage, the hand or catch (r 11 ) is thrown out of the teeth of the 
ratchet-wheel by the arm of the counter-faller, which then comes 
in contact with another arm (t 2 ) of the butterfly, the end of which 
extends lower down than the arm (S 2 ), and low enough to be 
struck by the arm of the counter-faller, when it is not under the 
action of the tension of the threads. The catch or hand then 
remains out, until the tension of the threads again requires the 
motion of the spindle to be reduced. The butterfly is connected 
with a hand-catch lever (m 2 ) that turns on a stud-pin (m 2 ), by 
which the attendant can throw the butterfly in and out of play. 
So soon as the base of the cop has been formed, the scroll form 
of the cam (m 1 ) gives the regular varying motions to the spin- 
dles to wind the cone of the cops, as fully pointed out in the 
general description. 

It has been stated that in finishing the cops, the threads are 
wound on harder at the point of the cops — this is effected in the 
following manner. On the shaft (e 11 ) which regulates the back- 
ing-off motion as described above, there is a hub (q 1 ) from which 
projects a crank arm (t l ), to the pin (S 1 ) of which is jointed by 
a link (r 1 ), a chain (p 1 ), the other end of which is jointed by a 
link (O 1 ) to the long arm of the lever (w l ), which forms the con- 
nection between the top rack (W 1 ) and the chain (l l ), which forms 
the connection between the top and main racks. This shaft, as 
heretofore described, is connected with the ratchet-wheel (N 2 ) 
which is operated by the catch or hand (M 2 ) of the lever (K 2 ) of 
the backing-off apparatus, and the chain (p 1 ) is of such length 
that it is wound up by the rotation of the shaft, until towards 
the completion of the cops, at which time it is drawn sufficiently 
tight to strike against a permanent arm (u 1 ) towards the end of 
the winding-in motion, which causes the lever (m 1 ) to turn on its 
axis, and by its connection to draw up the chain (I 1 ), and hence 
to increase the velocity of the rack (W 11 ), and, therefore, the ro- 
tation of the spindles which winds the threads on tighter — this 
operation gradually increases to the completion of the cops. On 
this same shaft (e 11 ) is placed the coping arm (y 2 ), the periphery 
of which acts on the lever (x 2 ), to which the coping rail or former 
(G 2 ) is jointed at (r) in manner well known to those acquainted 
with the construction of self-acting mules, and which, therefore, 



mason's self-acting mule. 413 

needs not to be described. This completes the whole series of 
motions, but it will be obvious that when one set of cops has been 
completed, the parts employed in giving the progressive move- 
ments, such as the shaft (e 11 ) that rotates the coping or forming 
cam (Y 2 ) winds the chain which carries the slide (e 1 ) of the back- 
ing-off apparatus, and the crank arm (t 1 ) that winds the chain (p 1 ) 
to increase the tension of the threads in finishing the points of 
the cop, and also the ratchet-wheels (Z 1 ) which governs the mo- 
tions of the slide (z 11 ) on the arm (V 2 ), by which the winding-on 
motion of the spindles is regulated to form the base of the cops, 
are to be turned back by hand to their original positions by the 
attendant preparatory to commencing a new set of cops. 

I have thus described the general character of the invention, 
and the manner of constructing and using the same, but before 
pointing out what I claim as my invention, I wish it to be dis- 
tinctly understood that I do not limit myself to the precise form 
and construction of the various parts employed, or to the pre- 
cise arrangement described, as I consider all mechanical equiva- 
lents as within the limits of my invention. 

What I claim, therefore, as my invention, and desire to secure 
by letters patent is — First, the disconnecting of the mechanism 
employed in running out the carriage and turning the draw roll- 
ers, from the mechanism which gives the whirling or spinning 
motion to the spindles, when the driving power is shifted from 
these the first series of motions, to enable the spindles to con- 
tinue their motion by inertia, independent of the other motions, 
by means of the clutch box (or its equivalent) which forms the 
connection between the three movements constituting the first 
series of motions, whereby the momentum of the spindles can be 
employed for preparing the parts for the backing-off motion, 
substantially as described. Second. The method of preparing 
the parts for the backing-off motion by means of the momentum 
of the spindles, by connecting them with the backing-off appa- 
ratus by means of the friction clutch, or any equivalent there- 
for, substantially as described. Third. The backing-off appa- 
ratus consisting of the combination of the top-sliding rack, which 
communicates motion to the spindles, the rocking shaft with its 
cam and spring brake and other appendages, and the connecting 
rod operated by the crank, all substantially as described. Fourth. 
The method of decreasing the backing-off motion to correspond 
with the increased length of the cops, by means of the slide in 
the intermediate arm of the connecting rod (between the two 
sections of the connecting rod), by means of which the rocking 



414 mason's self-acting mule. 

motion of the rock-shaft is gradually decreased, substantially as 
described. Fifth. Combining the train of wheels which actuates 
the backing-off motion of the carriage, by means of a clutch 
substantially as herein described, which admits of the necessary 
backing-off motion before the tooth of the clutch starts the car- 
riage, whether this be effected by a clutch or by any other means 
substantially the same. Sixth. Running in the carriage by 
means of a crank motion which actuates a sliding rack that com- 
municates the desired motion to the carriage, so as to start and 
arrest it gradually, substantially as described, to avoid any sud- 
den strain or jar upon the threads. Seventh. The method of 
communicating the winding-on motion to the spindles from the 
main' rack, which runs in the carriage by combining the said main 
rack with the top-sliding rack by means of a chain and scroll 
cam, or their equivalents, by means of which combination in 
connection with the form of the cam, the motions of the spin- 
dles so correspond with that of the carriage, as to wind the 
threads on the conical form of the cops as described. Eighth. 
The method of varying the winding-on motion of the spindles to 
form the base of the cops, by means of the slide and chain which 
vary the motions of the wheel that is attached to, and which 
rotates the scroll cam substantially as described, whether the 
slide be operated by the vibration of the arm on which it slides, 
or by any other means substantially as herein described. Ninth. 
The method of regulating the motion of the slide that varies the 
motions of the scroll cam of the winding-on motion, by means 
of what is termed the butterfly and its appendages, when this is 
acted upon by the counter-faller, operated by the tension of the 
threads, substantially as described. And, Tenth. The method 
of winding on the threads tighter at the points of the cops, 
when finishing them by means of the apparatus, which gives to 
the top-sliding rack, an increased motion towards the end of the 
operation, the said apparatus consisting of a chain which is con- 
nected with the chain that forms the connection between the 
main and top racks, and which is gradually wound up, and strikes 
against an arm towards the end of the operations of the mule, 
to shorten the connection between the two racks, and thus in- 
crease the winding-on motion of spindles as described. 



NIAGAEA THROSTLE, OR McCULLEY'S 
SPINNING FRAME. 

PLATES VII. VIII. 

This machine possesses the following advantages over all other 
hinds of Throstle or common Ring Spinning Frames : — 

1. A saving of one-half THE POWER consumed by the Spin- 
ning Frames now in general use. 

2. It occupies one-fifth less space. 

3. It is operated with one-third less LABOR compared with 
its product. 

4. It requires but one-half the Oil of other Spinning. 

5. All Banding is entirely dispensed with. 

6. The Repairs are not one-half that of frames running with 
bands. 

7. It is not affected by change of weather; therefore it uses a 
uniform amount of power. 

8. It can be operated at much greater speed and without a 
corresponding increase of power and wear and tear. 

9. It gives a stronger and more uniform motion to the spindle 
and a more even twist to the thread. 

10. It combines superior advantages for Spinning fine Worsted, 
with great speed and perfection. 

11. It is particularly well adapted for doublers and twisters for 
thread, and many are now in operation. 

There are many minor advantages with this, over all other 
spinning now in use. It does not throw off the oil — it is a much 
more durable machine, and gets rid of bands with all their ex- 
pense, annoyances, imperfections and uncertainties. It does not 
require that attention and skill in the overseer to regulate it, 
after it is adjusted to give the twist intended ; and when once 
adjusted, so it will remain and continue to operate. If required, 
the Spindles may be driven 10,000 revolutions per minute. 
Nearly two-thirds the power of a Cotton Mill is wanted to drive 
the spinning, and the great saving in power by this frame reduces 
the weight and expense of main gearing, shafting, pulleys, and 



416 NIAGARA THROSTLE. 

belts correspondingly. It can be readily changed from coarse 
to fine yarn. Either side of this frame may be operated indepen- 
dently of the other, and stopped at pleasure, without affecting 
the operation of the other side. 

These are believed to be fair statements of facts, which the 
operation of this machine with more than two years practical 
test fully confirms. 

These Spinning frames may be seen in operation, in many 
sections of the country. 

The novelty consists in the mode of driving the Spindles, 
Flyers, and Bobbins by friction pulleys instead of bands (the 
old way), as invented and patented by Francis McCulley, Jr. 
The lithograph represents a Ring Spinning Frame, in which the 
usual cylinders and bands are dispensed with, and the friction 
pulleys are introduced. The invention is as applicable to driving 
flyers, and also for Doublers and Twisters, and Worsted Frames. 
It may be applied to all kinds of throstle spinning, with similar 
advantages. It is very largely in operation, and with the univer- 
sal testimony of those using them, that the motion to the spindle 
is stronger, more regular and uniform driven by friction pulleys, 
than when driven by bands. There is a whirl made fast to the 
spindle, the underside of which is covered with leather, and rests 
upon the periphery of the pulley. These leathers will last for 
many years, and the spindles and bearings wear but very little, 
having no bands pulling them. 

Fig. 4, Plate VIII. is an end elevation, showing the arrange- 
ment for the gears and belts for driving the rolls and lifting motion 
for the rails. 

Fig. 1, Plate VII. is a front elevation, showing the rolls, 
spindles, and an edge view of the friction- disks for driving the 
spindles. These disks and the whirls running upon them consti- 
tute the parts patented by McCulley. 

Fig. 3, Plate VIII. is a vertical section of the machine through 
the centre of one section, showing the roller-stands ; the manner 
of weighing top-rolls by the weights ; the bearings for the side- 
shafts, stands for the spindles, guide-rod for raising top or ring 
rail. 

Fig. 2, Plate VIII. is an end elevation. 

Further information may be obtained of the Agents, Miner & 
Pitman, 171 Milk Street, Boston, Mass., or of Arthur M. East- 
man, of Boston, the proprietor of the patent, and who has been 
chiefly instrumental in bringing this admirable machine to its 
present state of perfection. 



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INDEX 



TO THE 



PRACTICAL MODE CALCULATOR, 



BY 



OLIVEE BTENE, 



CIVIL, MILITARY, AND MECHANICAL ENGINEER. 



PHILADELPHIA: 
PUBLISHED BY HENRY CAREY BAIRD, 

(SUCCESSOR TO B. L. CAREY,) 

SOUTH-EAST CORNER MARKET AND FIFTH STREETS. 

1851. 



INDEX. 



Abbreviation of the reduction of deciinals,l7. 

Abrasion, limits of, 301. 

Absolute resistances, 288. 

Absolute strength of cylindrical columns, 274. 

Accelerated motion, 386. 

Accelerated motion of wheel and axle, 419. 

Acceleration, 415. 

Acceleration and mass, 422. 

Actual and nominal horse power, 240. 

Addition of decimals, 22. 

Addition of fractions, 20. 

Adhesion, 297. 

Air, expansion of, by heat, 173. 

Air that passes through the fire for each horse 
power of the engine, 210. 

Air, water, and mercury, 355. 

Air-pump, 254. 

Air-pump, diameter of, eye of air-pump cross 
head, 145. 

Air-pump machinery, dimensions of several 
parts of, 144. 

Air-pump strap at and below cutter, 147. 

Air-pump studs, 144. 

Ale and beer measure, 8. 

Algebra and arithmetic, characters used in, 12. 

Algebraic quantities, 134. 

Alloys, strength of, 287. 

Ambiguous cases in spherical trigonometry, 
381. 

Amount of effective power produced by steam, 
266. 

Anchor rings, 90. 

Angle iron, 91, 408, 409, 410. 

Angles of windmill sails, 445. 

Angles, measurement of, by compasses only, 
382. 

Angular magnitudes, 359. 

Angular magnitudes, how measured, 373. 

Angular velocity, 412. 

Apothecaries - ' weight, 6. 

Apparent motion of the stars, 353. 

Application of logarithms, 334. 

Approximating rule to find the area of a seg- 
ment of a circle, 67. 

Approximations for facilitating calculations, 
55. 

Arc of a circle, to find, 49. 

Arc of one minute, to find the length of, 361. 

Arc, the length of which is equal to the ra- 
dius, 357. 

Architecture, naval, 453. 

Arcs, circular, to find the lengths of, 68. 

Area of segment and sector of a circle, 51. 

Area of steam passages, 220. 

Areas of circles, 57. 

Areas of segments and zones of circles, 64, 
65, 66, 67. 

Arithmetic, 10. 

Arithmetical progression, to find the square 
root of numbers in, 126. 

Arithmetical solution of plane triangles, 366. 
2x2 



Arithmetical proportion and progression, 35 

to 38. 
Ascent of smoke and heated air in chimneys, 

208. 
Atmospheres, elastic force of steam in, 195, 

196. 
Atmospheric air, weight of, 356. 
Average specific gravity of timber, 396. 
Avoirdupois weight, 6. 
Axle and wheel, 417. 
Axle of locomotive engine, 168, 169. 
Axle-ends or gudgeons, 301. 
Axles, friction of, 298, 300. 

Balls of cast iron, 407. 

Bands, ropes, &c, 267. 

Bar iron, 400. 

Beam, 151. 

Beam, the strongest, 276. 

Bearings of water wheels, 285. 

Bearings or journals for shafts of various 
diameters, 287. 

Beaters of threshing machine, 445. 

Before and behind the piston, 232. 

Blast pipe, 171. 

Blistered steel, 281. 

Blocks, cords, ropes, sheives, 428. 

Bodies, cohesive power of, 175. 

Bodies moving in fluids, 324. 

Boiler, 171. 

Boiler plate, experiments on, at high tempe- 
ratures, 220. 

Boiler plates, 403. 

Boilers, 256 and 257. 

Boilers of copper and iron, diminution of 
the strength of, 219. 

Boilers, properties of, 215. 

Boilers, strength of, 218. 

Bolts and nuts, 406. 

Bolts, screw and rivet, 220. 

Boring iron, 445. 

Bossut and Michelloti, experiments on the 
discharge of water, 319. 

Boyle of Cork, 200. 

Bramah's press, 427. 

Branch steam-pipe, 148. 

Brass, copper, iron, properties of, 280. 

Brass, round and square, 408. 

Breast wheels, 328. 

Breast and overshot wheels, maximum ve- 
locity of, 443. 

Buckets and shrouding of water wheels, 446. 

Building, to support with cast iron columns, 
293. 

Bushel, 5. 

Butt for air-pump, 146. 

Butt, thickness and breadth of, 14,3. 

Butt, to find the breadth of, 141. 

Byrne's logarithmic discovery, 340. 

Byrne's theory of the strength of materials, 
272. 

569 



570 



INDEX. 



Calculation in the art of ship-building, 453 
to 500. 

Canvas of vessels, 488, 500. 

Carriages, motion of, on inclined planes, 429. 

Carriages travelling on ordinary roads, 307. 

Carrier or intermediate wheels, 434. 

Carts on ordinary roads, 311. 

Cases in plane trigonometry, 363. 

Cast iron, 174. 

Cast iron pipes, 404. 

Centre of effort of sails, 483, 490. 

Centre of gravity, 175. 

Centre of gravity of displacement of a ship, 
456, 457, 458. 

Centre of gyration, 180. 

Centre of oscillation, 187. 

Centres of bodies, 386. 

Centres of gravity, gyration, percussion os- 
cillation, 391. 

Centripetal and centrifugal forces, 178, 450. 

Chain bridge, 412. 

Chimney, 171, 208, 257. 

Chimney, size of, 212. 

Chimney, to what height it may be carried 
with safety, 212. 

Circle, calculations respecting, 48, 49, 50, 53. 

Circle of gyration in water wheels, 444. 

Circles, 57 to 61. 

Circles, areas of, 57 to 63. 

Circular arcs, 68. 

Circular motion, 422. 

Circular parts of spherical triangles, 375. 

Circumference of a circle to radius 1, 361. 

Circumferences of circles, 57. 

Cloth measure, 7. 

Coefficient of efflux, 314. 

Coefficients of friction, 299. 

Cohesive strength of bodies, how to find, 281. 

Collision of railway trains, 452. 

Columns, comparative strength of, 294. 

Combinations of algebraic quantities, 134. 

Common fractions, 15. 

Common materials, 280. 

Complementary and supplementary arcs, 374. 

Compound proportion, 14. 

Condenser, 226. 

Condensing water, 223. 

Conduit pipes, discharge by, 322. 

Cone, 82. 

Conical pendulum, 185 to 187. 

Connecting rod, 140, 141, 253. 

Continuous circular motion, 432. 

Contraction by efflux, 316. 

Contraction of the fluid vein, 313. 

Contractions in the calculation of loga- 
rithms, 348. 

Copper boilers, 219. 

Copper, iron, and lead, 405. 

Cosine, to find, 361. 

Cosines, contangents, Ac, for every degree 
and minute in the quadrant, 540 to 576. 

Cosines, natural, 411. 

Cover on the exhausting side of the valve, 
in parts of the length of stroke, 231. 

Cover on the steam side, 226. 

Crane, 427. 

Crane, sustaining weight of, 285. 

Crank at paddle centre, 135. 

Crank axle, diameter of the outside bearings 
of, 168. 



Crank axle of locomotive, 169. 

Crank pin, 170, 252. 

Crank pin journal, 252. 

Crank pin journal, to find the diameter of, 139. 

Crank pin journal, to find the length of, 139. 

Cross head, 252. 

Cross head, to find the breadth of eye of, 139. 

Cross head, to find the depth of eye of, 139. 

Cross multiplication, 27. 

Cross tail, 253. 

Cube, 79. 

Cube and cube roots of numbers, 100 to 116. 

Cube root of numbers containing decimals, 
128. 

Cube root, to extract, 32. 

Cubes, 397 to 400. 

Cubes, to extend the table of, 128. 

Curve, to find the length of, by construction,72. 

Curves, to find the areas of, 453. 

Cuttings and embankments, 97. 

Cylinder side rods at ends, to find the diame- 
ter of, 143. 

Cylinders, 80, 397 to 400. 

Cylinders of cast iron, 404. 

Dams inclined to the horizon, 316. 

Decimal approximations for facilitating cal- 
culations, 55. 

Decimal equivalents, 56. 

Decimal fractions, 22. 

Decimal fractions, table of, 73. 

Decimals, addition of, 22. 

Decimals, division of, 24. 

Decimals, multiplication of, 23. 

Decimals, reduction of, 25, 26. 

Decimals, rule of three in, 27. 

Decimals, subtraction of, 23. 

Deflection of beams, 295. 

Deflection of rectangular beams, 294. 

Depth of web at the centre of main beam, 150. 

Destructive effects produced by carriages on 
roads, 311. 

Devlin's oil, 297. 

Diagram of a curve of sectional areas, 460. 

Diagram of indicator, 265. 

Diameter of cylinder, 251. 

Diameter of main centre journal, 143. 

Diameter of plain part of crank axle, 169. 

Diameter of the outside bearings of the crank 
axle, 168. 

Diameters of wheels at their pitch circle to 
contain a required number of teeth, 436. 

Dimensions of the several parts of furnaces 
and boilers, 254. 

Direct method to calculate the logarithm of 
any number, 346. 

Direct strain, 278. 

Discharge by compound tubes, 321. 

Discharge by different apertures from differ- 
ent heads of water, 318. 

Discharge of water, 446. 

Discharges from orifices, 426. 

Displacement of a ship when treated as a 
floating body, 455. 

Displacement of ships, by vertical and hori- 
zontal sections, 460, 500. 

Distance of the piston from the end of its 
stroke, when the exhausting port is shut 
and when it is open, 231. 

Distances, how to measure, 369. 



INDEX. 



571 



Division by logarithms, 336. 

Dodecaedron, 89. 

Double acting engines, rods of, 250. 

Double position, 44. 

Double table of ordinates, 457. 

Drainage of water through pipes, 325. 

Dr. Dalton, and his countryman, Dr. Young, 

of Dublin, 
Drums, 422. 

Drums in continuous circular motion, 432. 
Dry or corn measure, 8. 
Duodecimals, 27. 
Dutch sails of windmills, 333. 
D. valves, 233. 
Dynamometer, used to measure force, 269. 

Eduction ports, 171. 

Effective discharge of water, 314. 

Effective heating surface of flue boilers, 256. 

Effects of carriages on ordinary roads, 311. 

Elastic force of steam, 188. 

Elastic fluids, 205. 

Elliptic arcs, 69, 70, 71, 72. 

Embankments and cuttings, 97. 

Endless screw, 431. 

Engineering and mechanical materials, 386. 

Engine, motion of steam in, 206. 

Engine tender tank, 92. 

Enlargements of pipes, interruption of dis- 
charge by, 321. 

Evolution, 29. 

Evolution by logarithms, 339. 

Eye, diameter of, 251. 

Eye of crank, 136. 

Eye of crank, to find the length and breadth 
of large and small, 142. 

Eye of round end of studs of lever, 143. 

Examples on the velocity of wheels, drums, 
and pulleys, 438. 

Exhaust port, 230. 

Expanded steam, 236. 

Expansion, 237. 

Expansion, economical effect of, 216. 

Experiments on the strength and other pro- 
perties of cast iron, 174. 

Explanation of characters, 12. 

Extended theory of angular magnitude, 374. 

Exterior diameter of large eye, 252. 

Extraction of roots by logarithms, 339. 

Eall of water, 444. 

Feed pipe, 150. 

Feed water, 222. 

Felloes of wheels, 309. 

Fellowship, or partnership, 41. 

Fire-grate, 171, 214. 

Fitzgerald, 264, 269. 

Flange, 91. 

Flat bar iron, 407. 

Flat iron, 400. 

Flexure by vertical pressure, 292. 

Flexure of revolving shafts, pillars, Ac, 296. 

Flues, 256. 

Flues, fires, and boilers, 217. 

Fluids, the motion of elastic, 205. 

Fluids, to find the specific gravity of, 392. 

Fluids, the pressure of, 448. 

Fluid vein, contraction of, 313. 

Foot-valve passage, 149. 

Force, 267. 

Force, loss of, in steam pipes, 221. 



Force of steam, 188. 

Forces, centrifugal and centripetal, 178, 450. 

Fore and after bodies of immersion, 456, 460. 

Form, the strongest, 275. 

Formulas for the strength of various parts 
of marine engines, 251. 

Formulas to find the three angles of a sphe- 
rical triangle when the three sides are 
given, 385. 

Formula, very useful, 271. 

Fourth and fifth power of numbers, 129. 

Fractions, common, 15. 

Fractions, reduction of, 16, 17, 18, 19. 

Fractions, addition of, 20. 

Fractions, subtraction of, 21. 

Fractions, multiplication of, 21. 

Fractions, division of, 21. 

Fractions, the rule of three in, 21. 

Fractions, decimal, 22. 

Fractions, table of, 73. 

Fractions, addition contracted, 78. 

Fracture, 292. 

Franklin Institute, 172, 219. 

French litre, 355. 

French measures, 5, 6. 

French metre, 347. 

Friction, 238. 

Friction, coefficents of, 300. 

Friction of fluids, 325. 

Friction of rest and of motion, 267. 

Friction of steam engines of different modi- 
fications, 302. 

Friction of water against the sides of pipes, 321 . 

Friction of water-wheels, windmills, &c, 267. 

Friction, or resistance to motion, in bodies 
rolling or rubbing on each other, 297. 

Friction, laws of, 298. 

Frustums, 83. 

Frustum of spheroid, 87. 

Furnace, 256. 

Furnace room, 213. 

Gallon, 5. 
Gases, 394. 
Geering, 422. 

General and universal expression, 376. 
General observations on the steam engine,259. 
General trigonometrical solutions, 365, 369. 
Geometrical construction, 362. 
Geometrical construction of the proportion 

of the radius of a wheel to its pitch, 440. 
Geometrical proportion and progression, 38. 
Gibs and cutter, 140, 253. 
Gibs and cutter through air pump cross-head, 

146, 147. 
Gibs and cutter through cross-tail and 

through butt, 141. 
Gibs and cutter, to find the thickness and 

breadth of, 143. 
Girder, 275. 

Girth, the mean in measuring, 94. 
Glenie, the mathematician, 287. 
Globe, 85. 
Grate surface, 255. 
Gravity, centre of, 175, 386. 
Gravity, specific, 391. 
Gravity, weight, mass, 386. 
Gudgeons, 420. 
Gyration, centre of, 180, 390. 
Gyration, the centre of different figures and 

'bodies, 181. 



572 



INDEX. 



Heads of water, 318. 

Heating surface, 256. 

Heating surface of boilers, 215. 

Heights and discharges of water, 319. 

Heights and distances, 359. 

Height of chimneys, 210. 

Height of metacentre, 470, 483. 

Hewn and sawed timber, 95. 

Hexagon, heptagon, 48. 

High pressure and condensing engines, 234. 

Hollow shafts, to find the strength of, 284. 

Horizontal distance of centre of radius bar, 

246, 247. 
Horse power, 240. 
Horse power of an engine, dimensions made 

to depend upon the nominal horse power 

of an engine, 147. 
Horse power of pumping engines, 447. 
Horse power, tables of, 243, 244. 
Hot blast, 174. 
Hot liquor pumps, 446. 
Hydraulic pressure working machinery, 330. 
Hydraulics, 267, 312. 
Hydrogen, weight of, 356. 
Hydrostatic press, 448. 
Hyperboloid, 88. 

Hyperbolic logarithms, 130 to 133. 
Hyperbolic logarithms, how to calculate, 353. 
Hypothenuse of a spherical triangle, to find, 

378. 
Hypothenuse, 47. 

IcOSAEDRON, 89. 

Immersed portions of a ship, to calculate, 
456. 

Immersion and emersion, 493. 

Impact, 449. 

Impinging of elastic and inelastic bodies, 
452. 

Inaccessible distances, 372. 

Inches in a solid foot, 96. 

Inclined plane, 428, 429, 430. 

Inclination of the traces of ordinary car- 
riages, 311. 

Inclinations, discharge of a 6-inch pipe at 
several, 326. 

Increase of efiiciency arising from working 
steam expansively, 262. 

Index of logarithms, 334. 

Indicator, 264, 265. 

Indicator, the amount of the effective power 
of steam by, 266. 

Induction ports, 171. 

Inelastic bodies, 449. 

Influence of pressure, velocity, width of fel- 
loes, and diameter of wheels, 309. 

Initial plane, 456, 480, 500. 

Initial velocity with a free descent, 388. 

Injection pipe, 150. 

Inside discharging turbine, 330. 

Integer, 10. 

Integers, to find the square root of, 125. 

Interest, simple, 42. 

Interest, compound, 43. 

Involution, 28. 

Involution, or the raising of powers by loga- 
rithms, 338. 

Hregular polygons, 54. 

Iron, forged and wrought, 272. 

Iron plates, 403. 

Iron, properties of, 175. 



Iron, strength of, 173. 

Iron, taper and parallel, angle and T, rail- 
way and sash, 408, 411. 

Jet, specific gravity of, 394. 

Journal of cross-head, to find diameter of,139. 

Journal of cross-head, to find the length 

of, 139. 
Journal, the mean centre, to find the diameter 

of, 143. 
Journal, strain of, 252. 
Journals for air-pump cross-head, 145. 
Journals for shafts of various diameters, 287. 
Julian year, 357. 
Juste Byrge, the inventor of logarithms, 133. 

Kane, Fitzgerald, 269. 
Keel and keelson, 433 to 500. 
Kilometre, 5. 
Kilogramme, 6. 
Knots, nodes, &c, 412. 

Lathe spindle wheel, 435. 

Laying off of angles by compasses only, 384. 

Leg of a spherical triangle, to find, 377. 

Length of crank pin of locomotive, 170. 

Length of paddle-shaft journal, 138. 

Length of stroke, 227, 251. 

Lengths that may be given to stroke of the 

valve, 229. 
Lengths of circular arcs, 68. 
Lever, 426. 

Light displacement, 459. 
Line of direction, 390. 
Link next the radius bar, 242. 
Living forces, or the principle of vis viva,270. 
Load immersion, 456, 457. 
Load-water line, 456, 470. 
Locomotive engine, parts of the cylinder, 171. 
Locomotive engine, diameter of the outside 

bearings for, 163. 
Locomotive engine, dimensions of several 

moving parts, 171. 
Locomotive engine, dimensions of several 

pipes, 171. 
Locomotive engine, parts of the boiler, 171. 
Locomotive engine, tender tank, 92. 
Locomotive and other engines, 233. 
Logarithmic calculations, 376. 
Logarithmic calculations of the force of 

steam, 190 to 193. 
Logarithmic sines, tangents, and secants for 

every minute in the quadrant, 540, 576. 
Logarithms applied to angular magnitudes, 

359. 
Logarithms, hyperbolic, 130. 
Logarithms of the natural numbers from 1 

to 100000 by the help of differences, 503 

to 540. 
Logarithms, the application of, 334. 
Long measure, 7. 
Longitudinal distance of the centre of gravity 

of displacement, 470, 500. 
Loss of force by the decrease of temperature 

in the steam pipes, 221. 
Low pressure engines, 243. 
Lunes, 54. 

Machinery, elements of, 425. 
Machinery worked by hydraulic pressure, 
330. 



INDEX. 



573 



Mai or and minor diameters of cross-head, 

253. 
Main beam at centre, 249. 
Malleable iron, 396. 
Marble, 288. 
Marine boilers, 217. 
Mass, 267. 

Mass, gravity, and weight, 3S6. 
Mass of a body, to find, when the weight is 

given, 389. 
Materials employed in the construction of 

machines, 267. 
Materials, their properties, torsion, deflexion, 

Ac, 267. 
Maximum accelerating force, 421. 
Maximum velocity and power of water 

wheels, 443. 
Measures and weights, 5. 
Measurement of angular magnitudes, 374. 
Measurement of angles by compasses only, 

382. 
Mechanical effect, 417. 
Mechanical powers, 422. 
Mechanical power of steam, 261. 
Mensuration of solids, 79. 
Mensuration of timber, 93. 
Mensuration of superficies, 45. 
Mercury, density of, 350. 
Mercury, to calculate the force of steam in 

inches of, 201. 
Method to calculate the logarithm of any 

given number, 340. 
Metaeentre, 453, 466, 483. 
Metre, 5. 
Midship, or greatest transverse section, 460, 

488. 
Millboard, 405. 
Millstones, 445. 
Millstones, strength of, 451. 
Modulus of elasticity, 278. 
Modulus of logarithms, 343. 
Modulus of torsion and of rupture, 279. 
Moment of inertia, 412. 
Motion of elastic fluids, 205. 
Motion of steam in an engine, 206. 
Multiplication of decimals, 23. 
Multiplication of fractions, 21. 
Multiplication by logarithms, 335. 
Musical proportion, 40. 

Natural sines, cosines, tangents, cotangents, 

secants, and cosecants, to every degree of 

the quadrant, 411. 
Naval architecture, 453. 
New method of multiplication, 342. 
Nitrogen, weight of, 356. 
Nominal horse power, tables of, for high and 

low pressure engines, 243, 244. 
Notation and numeration, 10. 
Notation, trigonometrical, 359. 
Number corresponding to a given logarithm, 

351. 
Number of teeth, or the pitch of small 

wheels, 435. 
Numbers, fourth and fifth powers of, 129. 
Numbers, logarithms of, 540, 756. 
Numbers, reciprocals of, 73 to 78. 
Numbers, squares, cubes, &c, of, 100 to 116. 
Numeral solution of the several cases of 

trigonometry, 361. 
Nuts and bolts, 406. 



Oak, Dantzio, 280. 

Obelisk, to find the height of, 371. 

Oblique triangles, 368. 

Observatory at Paris g = 9-80896 metres,346. 

O'Byrne's turbine tables, 331. 

Octagon, 48. 

Octaedron, 89. 

O'Neill's experiments, 447. 

O'Neill's rules employed in the art of ship- 
building, 454. 

Opium, specific gravity of, 394. 

Orders of lever, 426. 

Ordinates employed in the art of ship-build- 
ing, 455, 456, 458, 500. 

Orifices and tubes, discharge of water by, 312. 

Orifices, rectangular, 314. 

Oscillation, centre of, 187, 391. 

Outside bearings of crank axle, 168. 

Outside discharging turbines, 331. 

Overshot wheels, 329. 

Overshot wheels, maximum velocity of, 443. 

Ox-hicle, 299. 

Oxygen, 214, 356. 

PADDLE-shaft journal, 137, 251. 

Paraboloid, 88. 

Parabolic conoid, 88. 

Parallel angle iron, 409. 

Parallel motion, 242 to 246. 

Parallelogram of forces, 422. 

Parallelopipedon, 80. 

Partnership, 41. 

Partial contraction of the fluid vein, 316. 

Passages, area of steam, 220. 

Peclet's expression for the velocity of smoke 

in chimneys, 213. 
Pendulums, 183, 391. 
Pendulum, conical, 184. 
Pendulums, vibrating seconds at the level of 

the sea in various latitudes, 393. 
Percussion, centre of, 391. 
Periodic time, 179. 

Permanent weight supported by beams, 284. 
Permutations and combinations, 44. 
Pillars, strength of, 293. 
Pinions and wheels in continuous circular 

motion, 432. 
Pipes, discharge and drainage of water 

through, 321, 322, 325. 
Pipes of cast iron, 395. 
Pipes for marine engines, 149. 
Piston, 251. 

Piston of steam engine, 414. 
Piston rod, 140, 171, 253. 
Piston rod of air-pump, 146. 
Pitch circle, 436. 
Pitch of teeth, 441. 
Pitch of wheels, 435, 439. 
Plane triangles, solution of, 364, 365. 
Plane trigonometry, 359. 
Planks, deals, 94. 
Polygons, 47, 48. 
Polygons, irregular, 54. 
Port, upper and lower, 229. 
Position, double, 44. 
Position, single, 43. 
Pound, 5. 

Power, actual and nominal, 241. 
Power and properties of steam, 261. 
Power that a cast-iron wheel is capable of 

transmitting, 442. 



574 



INDEX. 



Power of shafts, 294. 

Practical application of the mechanical 
powers, 425. 

Practical limit to expansion, 261. 

Practical observations on steam engines, 260. 

Principle of virtual velocities, 423. 

Prism, 80. 

Prismoid, 85. 

Properties of bodies, 401. 

Proportional dimensions of nuts and bolts, 
406. 

Proportion, 14. 

Proportion, musical, 40. 

Proportion and progression, arithmetical, 35 
to 38. 

Proportion and progression, geometrical, 38 
to 40. 

Proportion, or the rule of three by loga- 
rithms, 338. 

Proportion of wheels for screw-cutting, 433. 

Proportions of boilers, grates, &c, 213. 

Proportions of the lengths of circular arcs, 68. 

Proportions of undershot wheels, 328. 

Pulleys, 422, 427. 

Pump and pumping engines, 446. 

Pumping engines, 422. 

Pyramid, 82. 

Pyrometer, 63. 

Quadrant, 359. 

Quadrant, log. sines, cosines, &c, for every 
minute in, 540, 576. 

Quadrant, natural sines and cosines for 
every degree of, 411. 

Quadrant, to take angles with, 370. 

Quantities, known and unknown, 134. 

Quantity of water that flows through a cir- 
cular orifice, 313, 319. 

Quiescence, friction of, 299. 

Radius bar, 242. 

Radius bar, length of, corrected, 248. 

Radius of the earth at Philadelphia, 356. 

Radius of gyration, 412. 

Radius, length of, in degrees, 357. 

Rails, temporary, 411. 

Railway carriage, 268. 

Railway iron, 410. 

Raising of powers by logarithms, 338. 

Reciprocals of numbers, 73 to 78. 

Recoil, 449. 

Rectangle, rhombus, rhomboides, to find 
the areas of, 45, 46. 

Reduction of fractions, 16, 17, to 19, 20. 

Regnault's experiments on oxygen, &c, 356. 

Regular bodies, 90. 

Relative capacities of the two bodies under 
the same displacement, 456, 470. 

Relative strength of materials to resist tor- 
sion, 294. 

Revolving shaft, 250. 

Riga fir, 290. 

Right-angled spherical triangles, 374. 

Ring, circular, to find the area of, 53. 

Ring, cylindrical, 90. 

Roads, traction of carriages on, 307. 

Rolled iron, 395. 

Roman notation, 11. 

Rope, strength of, 282. 

Ropes, bands, &c, 267. 

Ropes, blocks, pulleys, 428. 



Ropes, stiffness of, resistance of, to bendin 

302. 
Ropes, tarred and dry, 304, 306. 
Rotative engines, 260. 
Rotation, moment of, 414. 
Rotation of a body about a fixed axis, 416. 
Rotations of millstones, 452. 
Round and rectangular bars, strength of, 2S1. 
Round bar-iron, 403. 
Round steel and brass, 408. 
Rules for pumping engines, 448. 
Rule of three, 13. 

Rule of three by logarithms, 338. $ 

Rule of three in fractions, 21. 1 

Rupture, 272. j 

Safety valves, 149, 150, 224. 

Sails of windmills, 332. 

Sash iron, 410. 

Scales of chords, how to construct, 360. 

Scale of displacement, 465. 

Scantling, 95. 

Screw cutting by lathe, 433. 

Screw, power of, 430. 

Screw, to cut, 434. 

Sectional area measured, 456. 

Segments of circles, 64 to 67. 

Sheives, cords, blocks, 428. 

Ship-building and naval architecture, 453. 

Sidereal day, 9. 

Side lever, to find the depth across the centre 
of, 144. 

Side rod, 246, 254. 

Side rod of air-pump, 146. 

Sines, cosines, &c, 411. 

Sines, tangents and secants, 359. 

Singular phenomena, 237. 

Sleigh, 268. 

Slide valve, 225. 

Slide valve, a cursory examination of, 232. 

Slopes lj to 1, 2 to 1, and 1 to 1, 97. 

Sluice board, 316. 

Smoke and heated air in chimneys, 202. 

Solid inches in a solid foot, 96. 

Solids, mensuration of, 79. 

Space described by a body during a free de- 
scent in vacuo, 388. 

Specific gravity, 386, 391. 

Sphere, 85. 

Spheres, 397 to 400. 

Spheroid, 86, 87, 88. 

Spherical trigonometry, 373. 

Spheroidal condition of water in boilers, 236. 

Spindle and screw wheels, 434. 

Square, to find the area of, 45. 

Square and sheet iron, 402. 

Squares and square roots of numbers, 100 
to 116. 

Square root, 30. 

Square root of fractions and mixed numbers, 
31. 

Square measure, 6. 

Stability, 459, 499. 

Stars, apparent motion of, 353. 

Statical moment, 417. 

Steam engine, 135. 

Steam dome, 171. 

Steam passages, 220. 

Steam pipes, loss of force in, 222. 

Steam port, 147, 148. 

Steam room, 259. 



INDEX. 



575 



Steam, elastic force of, 188 to 202. 

Steam, temperature of, pressure of, 172. 

Steam, volume of, 202 to 206. 

Steam, weight of, 204. 

Steel, 408. 

Stiffness of a vessel under canvas, 485. 

Stiffness of ropes, 302, 306. 

Stowage, 503. 

Stowing the hold of a vessel, 453, 456. 

Strap at cutter, 141. 

Strap, mean thickness of, at and before cut- 
ter, 143. 

Strength of bodies, 282. 

Strength of boilers, 218. 

Strength of materials, 173, 271. 

Strength of rods when the strain is wholly 
tensile, 250. 

Strength of the teeth of cast iron wheels, 437. 

Studs of lever, 143. 

Stud-wheel and pinion, 434. 

Subtraction of decimals, 23. 

Subtraction of fractions, 21. 

Table by which to determine the number of 
teeth or pitch of small wheels, 435. 

Table containing the circumferences, squares, 
cubes, and areas of circles, from 1 to 100, 
advancing by a tenth, 57, 58, 59, 60 to 
63. 

Table containing the weight of columns of 
water, each one foot in length, in pounds 
avoirdupois, 401. 

Table containing the weight of square bar 
iron, 402. 

Table containing the surface and solidity of 
spheres, together with the edge of equal 
cubes, the length of equal cylinders, and 
weight of water in avoirdupois pounds, 
397. 

Table containing the weight of flat bar iron, 
400. 

Table containing the specific gravities and 
other properties of bodies; water the stand- 
ard of comparison, 401. 

Table containing the weight of round bar 
iron, 403. 

Table containing the weights of cast iron 
pipes, 404. 

Table containing the weight of solid cylin- 
ders of cast iron, 404. 

Table containing the weight of a square foot 
of copper and lead, 405. 

Table for finding the weight of malleable 
iron, copper, and lead, 405. 

Table for finding the radius of a wheel when 
the pitch is given, or the pitch when the ra- 
dius is given, for any number of teeth, 439. 

Table for the general construction of tooth 
wheels, 442. 

Table for breast wheels, 329. 

Table of polygons, 48. 

Table of decimal approximations for facili- 
tating calculations, 55. 

Table of decimal equivalents, 56. 

Table of the areas of the segments and zones 
of a circle of which the diameter is unity, 
64, 65, 66, 67. 

Table of the proportions of the lengths of 
semi-elliptic arcs, 69, 70, 72. 

Table of flat or board measure, 93. 

Table of solid timber measure, 94. 



Table of reciprocals of numbers, or of the 
decimal fractions corresponding to com- 
mon fractions, 71 to 77, 78. 

Table of weights and values in decimal 
parts, 79. 

Table of regular bodies, 90. 

Table of the cohesive power of bodies, 175. 

Table of hyperbolic logarithms, 130 to 133. 

Table of the pressure of steam, in inches of 
mercury at different temperatures, 172. 

Table of the temperature of steam at differ- 
ent pressures, in atmospheres, 172. 

Table of the expansion of air by heat, 173. 

Table of the strength of iron, 173. 

Table of the superficial and solid content of 
spheres, 96. 

Table of solid inches in a solid foot, 96. 

Table of squares, cubes, square and cube 
roots, of numbers, 100, 101, 116, 125. 

Table of cover on the exhausting side of the 
valve in parts of the stroke and distance 
of piston from the end of its stroke, 231. 

Table of the proportions of the lengths of 
circular arcs, 68. 

Table of the fourth and fifth power of num- 
bers, 129. 

Table of the properties of different boil- 
ers, 215. 

Table of the economical effects of expan- 
sion, 216. 

Table of the comparative evaporative power 
of different kinds of coal, 218. 

Table of the cohesive strength of iron boiler 
plate at different temperatures, 219. 

Table of diminution of strength of copper 
boilers, 219. 

Table of expanded steam, 239. 

Table of the proportionate length of bearings, 
or journals for shafts of various diameters, 
287. 

Table of tenacities, resistances to compres- 
sion and other properties of materials, 
288. 

Table of the strength of ropes and chains, 
288. 

Table of the strength of alloys, 289. 

Table of data of timber, 289. 

Table of the properties of steam, 261. 

Table of the mechanical properties of steam, 
263. 

Table of the cohesive strength of bodies, 281. 

Table of the strength of common bodies, 283. 

Table of torsion and twisting of common ma- 
terials, 286. 

Table of the length of circular arcs, radius 
being unity, 63. 

Table of experiments on iron boiler plate at 
high temperature, 220. 

Table of the absolute weight of cylindrical 
columns, 274. 

Table of flanges of girders, 276. 

Table of mean pressure of steam at different 
densities and rates of expansion, 239. 

Table of nominal horse power of high pres- 
sure engines, 244. 

Table of nominal horse power of low pres- 
sure engines, 243. 

Table of dimensions of cylindrical columns 
of cast iron to sustain a given load with 
safety, 293. 

Table of strength of columns, 294. 



576 



INDEX. 



Table of comparative torsion, 294. 

Table of the depths of square beams to sup- 
port from 1 cwt. to 14 tons, 295, 296. 

Table of the results of experiments on fric- 
tions, with unguents interposed, 299, 300. 

Table of the results of experiments on the 
gudgeons or axle-ends in motion upon their 
bearings, 301. 

Table of friction, continued to abrasion, 301. 

Table of friction of steam engines of differ- 
ent modifications, 302. 

Table of tarred ropes, 303. 

Table of white ropes, 305. 

Table of dry and tarred ropes, 306. 

Table of the pressure and traction of car- 
riages, 308. 

Table of traction of wheels, 309. 

Table of the ratio of traction to the load, 
310. 

Table of the coefficients of the efflux through 
rectangular orifices in a thin vertical plate, 
315. 

Table of the coefficients of efflux, 315. 

Table of comparison of the theoretical with 
the real discharges from an orifice, 317. 

Table of discharge of tubes of different en- 
largements, 322. 

Table of the comparison of discharge by pipes 
of different lengths, 323. 

Table of the comparison of discharge by ad- 
ditional tubes, 323. 

Table of the friction of fluids, 325. 

Table of discharges of a 6-inch pipe at seve- 
ral inclinations, 326. 

Table of the velocity of windmill sails, 333. 

Table of outside discharging turbine, 331. 

Table of inward discharging turbines, 332. 

Table of peculiar logarithms, 340. 

Table of useful logarithms, 345. 

Table of the specific gravity of various sub- 
stances, 394. 

Table of the weight of a foot in length of flat 
and rolled iron, 395. 

Table of the weight of cast iron pipes, 395. 

Table of the weight of one foot in length of 
malleable iron, 396. 

Table of comparison, 396. 

Table of the weight of a square foot of sheet 
iron, 402. 

Table of the weight of a square foot of boiler 
plate from | of an inch to 1 inch thick, 403. 

Table of the weights of cast iron plates, 403. 

Table of the weight of mill-board, 405. 

Table of the weight of wrought iron bars, 406. 

Table of the proportional dimensions of nuts 
and bolts, 406. 

Table of the specific gravity of water at dif- 
ferent temperatures, 406. 

Table of the weight of cast iron balls, 407. 

Table of the weight of flat bar iron, 407. 

Table of the weight of square and round 
brass, 408. 

Table of taper T iron, 410. 

Table of sash iron, 410. 

Table of rails of equal top and bottom, 410. 

Table of temporary rails, 411. 

Table of natural sines, cosines, tangents, co- 
tangents, secants, and cosecants, to every 
degree of the quadrant, 411. 

Table of inclined planes, showing the ascent 
or descent the yard, 430. 



Table of the weight of round steel, 408. 

Table of parallel angle iron of equal sides, 408. 

Table of parallel angle iron of unequal sides, 
409. 

Table of taper angle iron of equal sides, 409. 

Table of parallel T iron of unequal width and 
depth, 409. 

Table of change wheels for screw-cutting, 
435. 

Table of the diameters of wheels at their 
pitch circle, to contain a required number 
of teeth, 436. 

Table of the angle of windmill sails, 445. 

Table of the logarithms of the natural num- 
bers, from 1 to 100000, by the help of dif- 
ferences, 502 to 540. 

Table of log. sines, cosines, tangents, cotan- 
gents, secants and cosecants, for every de- 
gree and minute in the quadrant, 540 to 
576. 

Table of the strength of the teeth of cast iron 
wheels at a given velocity, 437. 

Table of approved proportions for wheels 
with flat arms, 441. 

Table showing the cover required on the 
steam side of the valve to cut the steam off 
at any part of the stroke, 228. 

Table showing the cover required, 227. 

Table showing the resistance opposed to 
the motion of carriages on different incli- 
nations of ascending or descending planes, 
429. 

Table showing the number of linear feet of 
scantling of various dimensions which are 
equal to a cubic foot, 95. 

Table showing the weight or pressure a beam 
of cast iron will sustain without destroying 
its elastic force, 292. 

Table showing the circumference of rope 
equal to a chain, 282. 

Table to correct parallel motion links, 248. 

Table of parallel T iron of equal depth and 
width, 410. 

Tables of cuttings and embankments, slopes, 
1 to 1; li to 1; and 2 to 1, 97. 

Tables of the heights corresponding to differ- 
ent velocities, 389. 

Tables of the mechanical properties of the 
materials most commonly employed in the 
construction of machines and framings, 
280. 

Tangents, 360. 

Tangents and secants, to compute, 362. 

Taper angle iron, 410. 

Teeth of wheels in continuous circular motion, 
432. 

Teeth of wheels, 422, 436. 

Temperature of steam, 172. 

Temperature and elastic force of steam, 188. 

Tension of chain-bridge, 414. 

Tetraedron, 89. 

Threshing machines, 445. 

Throttling the steam, 234. 

Timber measure, 93. 

Timber, to measure round, 95. 

Time, 7. 

Tonnage of ships, 461. 

Torsion, 279. 

Torsion and twisting, 286. 

Traction of carriages, 307. 

Transverse strength of bodies, 282. 



INDEX. 



577 



Transverse strain, 278. 

Transverse strain, time weight, 273. 

Trapezium, 47. 

Trapezoid, 47. 

Triangle, to find the area of, 46, 47. 

Trigonometry, 359. 

Trigonometry, spherical, 373. 

Troy weight, 7. 

Trussed beams, 291. 

Tubes, discharge of water through, 312. 

Tubular boilers, 257. 

Turbine water-wheels, 330. 

ULmrATE pressure of expanded steam, 236. 

Undecagon, 47. 

Undershot wheels, 327, 443. 

Unguents, 299. 

Ungulas, cylindrical, 81. 

Ungulas, conical, 83, 84. 

Unit of length, 5. 

Unit of weight, 5. 

Unit of dry capacity, 5. 

Units of liquids, 5. 

Units of work, 269, 297, 414, 4i!>. 

Universal pitch table, 442. 

Upper steam port, 229. 

Useful formula, 271. 

Use of the table of squares, cubes, &c, 127. 

Vacuum, perfect one, 235. 
Vacuum below the piston, 251. 
Vacuo, bodies falling freely in, 388. 
Valves, different arrangements of, 233. 
Valve, length of stroke of, in inches, 228. 
Valve shaft, 147. 
Valve, safety, 224. 
Valve, slide, 225. 
Valve spindle, 171. 
Vapour in the cylinder, 229. 
Vein, contraction of fluid, 330. 
Velocity, force, and work done, 267. 
Velocity of steam rushing into a vacuum, 207. 
Velocity of smoke in chimneys, 209, 213. 
Velocity of piston of steam engine, 266. 
Velocity of threshing machines, millstones, 

boring, &c, 445. 
Velocity of wheels on ordinary roads, 307. 
Venturi, experiments of, on the discharge of 

fluids, 421. 
Versed sine, tabular, 52. 
Versed sine of parallel motion, 244. 
Versed sine, 359. 



Vertical sectional areas, 454. 

Virtual velocities, 424. 

Vis viva, principle of, calculations on, 276, 

388. 
Volume of a ship immersed, 456. 
Volume of steam in a cubic foot of water, 

202, 205. 

Water, modulus of elasticity of, 190. 
Water level, 214. 
Water, feed and condensing, 223. 
Water, spheroidal condition of, in boilers,236. 
Water in boiler, and water level, 358. 
Water, discharge of, through different orifi- 
ces, 312, 318. 
Water wheels, 327. 

Water wheels, maximum velocity of, 443. 
Web of crank at paddle shaft centre, 136. 
Web of cross-head at middle, 139. 
Web of crank at pin centre, 142. 
Web at paddle centre, 252. 
Web of cross-head at journal, 140. 
Web of air-pump cross-head, 145. 
Wedge, 85. 

Wedge and screw, 430. 
Weights and measures, 5. 
Weights, values of, in decimal parts, 79. 
Weight, mass, gravity, 386. 
Weirs, and rectangular apertures, 314, 323. 
Wheel and axle, 417. 
Wheel and pinion, 427. 
Wheels, drums, pulleys, 438. 
Windmills, 332. 
Wine measure, 8. 
Woods, 280. 

Woods, specific gravity, 394. 
Work done, weight, 267. 
Wrought iron bars, 406. 

Yard, 5. 

Yacht, admeasurement of, 469 470. 

Yarns of ropes, 303. 

Yellow brass, 281. 

Yew, 280. 

Zinc, 280. 

Zinc, sheet, 288. 

Zone, spherical, 86. 

Zone, to find the area of a circular, 53. 

Zones of circles, to find the areas of, 64, 65, 



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